The radical is in simplest form when the radicand is not a fraction. The first law of exponents is x a x b = x a+b. This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions. Mathpoint.net includes great facts on simplest radical form calculator free, quadratic function and precalculus and other math subject areas. It will show the work by separating out multiples of the radicand that have integer roots. Write "Prompt N". Rational-equations.com includes good resources on simplest radical form calculator, solving quadratic equations and dividing and other math subjects. Simplify Square Root Calculator to find the simpliest form square root of any number. For the best answers, search on this site https://shorturl.im/awIM1. What is a simplified fraction? Simplest Radical Form Calculator Welcome to our Simplest Radical Form Calculator. A right software would be best option rather than a costly algebra tutor. Simplify a Term Under a Radical Sign. To find the product of two monomials multiply the numerical coefficients and apply the first law of exponents to the literal factors. Please enter the square root below that you want converted to simplest radical form: From simplify exponential expressions calculator to division, we have got every aspect covered. Enter the expression here Quick! ( A= Pert) A population numbers 11,000 organisms initially and decreases by 4.6% each year. calculator or notation come visit us at Mathisradical.com. Thanks to this 30 60 90 triangle calculator you find out that: shorter leg is 6.35 in - because a = b√3/3 = 11in * √3/3 ~ 6.35 in; hypotenuse is equal to 12.7 in - because c = 2b√3/3 = 2a ~ 12.7 in; area is 34.9 in² - it's the result of multiplying the legs length and dividing by 2 area = a²√3 ≈ 34.9 in Simplifying radicals is the process of manipulating a radical expression into a simpler or alternate form. Radical expression involves roots. Area of a triangle given sides and angle. ( A= Pert) A population numbers 11,000 organisms initially and decreases by 4.6% each year. It solves any algebra problem from your book. Free Radicals Calculator - Simplify radical expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. Procedures. Please leave them in comments. Radical 15 simplified gives step by step instructions on how to simplify the square root 15 in simplest radical form. Un-simplify the simplified radical form. I have a Texas Instruments TI-83 calculator and when I try to solve a radical it gives it in decimal form. Click the blue arrow to submit and see the result! Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Write as one number under the radicand. It has a double arrow on the key. From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x). If the calculator did not compute something or you have identified an error, please write it in Add your answer and earn points. A perfect square number has integers as its square roots. ... formulas and calculators . This tutorial demonstrates how to express answers in simplest radical form. After trying a number of software I found the Algebrator to be the best I have so far found . A population numbers 12,000 organisms initially and … The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. This online simplest radical form calculator simplifies any positive number to the radical form. I possibly could help you if you can be more specific and provide details about radical form calculator. Online Calculators > Math Calculators Square Root of 15 Simplified. Please enter the square root below that you want converted to simplest radical form: The calculator works for both numbers and expressions containing variables. Related Answers Use a calculator to find the value of A. meerkat18 meerkat18 So the problem ask to find the un simplified form of the simplified form of a radicals. Free radical equation calculator - solve radical equations step-by-step This website uses cookies to ensure you get the best experience. See also the Simplify Radical Expressions Calculator to simplify radicals instead of finding fractional (decimal) answers. The symbol is called a radical sign and indicates the principal square root of a number. Integer worksheets, simplified radical form., root calculator, boolean algebra on TI-89, percentage problems for ks2. It solves any algebra problem from your book . A value is in simplified radical form when the following conditions are met. Welcome to our Simplest Radical Form Calculator. Not sure which calculator you're using, but if it's the TI-30XS, which gives answers in the simplest radical form, there is a button in the lower right side of the keyboard, right above the enter button. BYJU’S online simplest form calculator tool makes calculations faster and easier where the value is displayed in a fraction of seconds. Trigonometry graph visual basic 6, importance of factoring a polynomial, nth roots calculator. The exponents on all prime factors in the radicand must be less than the index of the radical. To simplify your expression using the Simplify Calculator, type in your expression like 2 (5x+4)-3x. BYJU’S online simplest form calculator tool makes calculations faster and easier where the value is displayed in a fraction of seconds. To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x). Calculator Use. Simplifying Radical Expressions Calculator is a free online tool that displays a simplified form of the given radical expression or radical number. Use a calculator to find the value of A. The Simplest Form Calculator is a free online tool that displays the simplified form of the given fraction. To read our review of the Math Way -- which is what fuels this page's calculator, please go here . Numerator is found from 33/33 = 1 Denominator is found from 99/33 = 3 The fraction 33 / 99 reduced to the simplest form is 1 / 3. Special Triangles: Isosceles and 30-60-90 Calculator: This calculator performs either of 2 items: 1) If you are given a 30-60-90 right triangle, the calculator will determine the missing 2 sides. The following table contains the supported operations and functions: If you like the website, please share it anonymously with your friend or teacher by entering his/her email: In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. Enter the side that is known. The free calculator will solve any cube root. In this form a = b c \sqrt{a}=b\sqrt{c} a = b c , both b b b and c c c are positive integers, and c c c contains no perfect square factors other than 1 1 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Pythagorean theorem calculator is also known as hypotenuse calculator. Enter Number: 2) In addition, the calculator will allow you to same as Step 1 with a 45-45-90 right triangle. This page will help you to simplify an expression under a radical sign (square root sign). Type your expression into the box under the radical sign, then click "Simplify." Press "PRGRM" , go to the "I/O" tab and select "Prompt". Emaths.net gives insightful tips on simplified radical form calculator, factoring polynomials and syllabus for intermediate algebra and other math topics. Any time you actually have to have help with algebra and in particular with simplified radical form. Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)). To simplify square root using the calculator, just enter the term to simplify and apply the simplify_surd function. All suggestions and improvements are welcome. If you punch both quantities into a calculator you'll get the same number, $$-15.588457\ldots$$ This is the "real" meaning of the equation at hand, $$-3\sqrt{27} = -9\sqrt{3}.$$ The manipulation suggested by Zev leads you to a proof of this equality, but you should understand what it means: both expressions have the same value. Area of an equilateral triangle. No radicals in the denominator. We know that a radical expression is in its simplest form if there are … The following calculator can be used to simplify ANY expression with complex numbers. The symbol is called a radical sign and indicates the principal square root of a number. Solve for the simplified fraction. In order to simplify a fraction there must be: A number that will divide evenly into both the numerator and denominator so it can be reduced, or Go here for the next problem on our list. Right from convert radical form calculator to geometry, we have got every aspect covered. In cases where you require guidance on the quadratic formula or maybe functions, Algebra1help.com is without a doubt the right place to explore! Then type the letter "N" and … There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. To use the calcualor simply type any positive or negative number into the text box and hit the 'calculate' button. In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). Roots are often written using the radical symbol √. Simplifying Fractions Game … In cases where you have to have advice on exponential and logarithmic or perhaps lines, Alegremath.com is really the perfect site to check-out! Simplest radical form calculator Alegremath.com gives helpful tips on simplest radical form calculator, arithmetic and logarithmic and other algebra subject areas. RapidTables. Decimal Form Square Root of 24 in Decimal form rounded to nearest 5 decimals: 4.89898 Exponent Form Square Root of 24 written with Exponent instead of Radical: 24 ½ = 2 x 6 ½ Simplify Square Root of 25 The answer to Simplify Square Root of 24 is not the only problem we solved. Simplifying fractions calculator with mixed numbers. Second, divide both the numerator and denominator by the GCF. Simplified Radical Form. This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax 2 + bx + c = 0 for x, where a ≠ 0, using the quadratic formula. Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). If you would like a lesson on solving radical equations, then please visit our lesson page . The simplify calculator will then show you the steps to help you learn how to simplify your algebraic expression on your own. Square Roots, odd and even: There are 2 possible roots for any positive real number. Radical Simplifier Calculator . Please enter a number greater than 1. write sin x (or even better sin(x)) instead of sinx. Related Calculator. The Simplest Form Calculator is a free online tool that displays the simplified form of the given fraction. Mathway requires javascript and a modern browser. Note: this answer is kind of long so jump to picture to see a visual process. comments below. Send Me A Comment. To find the product of two monomials multiply the numerical coefficients and apply the first law of exponents to the literal factors. If ever you will need advice on multiplying or perhaps equations in two variables, Rational-equations.com is truly the right destination to take a look at! Alegremath.com gives helpful tips on simplest radical form calculator, arithmetic and logarithmic and other algebra subject areas. ... = Calculate × Reset. This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions. If you want to contact me, probably have some question write me using the contact form or email me on mathhelp@mathportal.org. Please ensure that your password is at least 8 characters and contains each of the following: You'll be able to enter math problems once our session is over. In order to find the simplest radical form of a square root, you need prime factorize the number. No fractions in the radicand. ( A= Pert) and fill in the question marks Use a calculator to find the value of A. If you would leave it in radical form that would be great! Thus, to calculate the following radical sqrt(99), enter simplify_surd(sqrt(99)) or directly sqrt(99), if the simplify_surd already appears , the result 3*sqrt(11) is returned. The square root pf a number can be simplified only if the number is divisible by a perfect square (other than 1). Was this calculator helpful? sqrt12 can be simplified because 12 is divisible by 4 -- a perfect square. * List of Perfect Squares It is also known as Nth root. Cross Product Calculator – An Efficient Way 16 hours ago; Area of a Rectangle – A Complete Lesson 17 hours ago; Average Rate of Change – A Quick Brief 19 hours ago; Change of Base Formula – Descriptive Guide 19 hours ago; distance formula calculator simplest radical form. To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). This online calculator will calculate the simplified radical expression of entered values. This type of radical is commonly known as the square root. Come to Polymathlove.com and figure out factoring trinomials, mixed numbers and a … If you get an error, double-check your expression, add parentheses and multiplication signs where needed, and consult the table below. Here we answer "What is the square root of 34 (√34) in simplest radical form?" Simplifying Radical Expressions Calculation. This website uses cookies to ensure you get the best experience on our website. Square Root of 15 Simplified to simplify the square root of 15 in radical form.Radical 15 simplified gives step by step instructions on how to simplify the square root 15 in simplest radical form. The Simplest Form Calculator is a free online tool that displays the simplified form of the given fraction. The square root symbol is also called as the Radical symbol (√). After this, press Solve Triangle306090. In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. GCF Calculator. We can therefore put 2 outside the radical and get the final answer to square root of 40 in simplest radical form as follows: 2√ 10 Simplest Radical Form Calculator Here you can submit another square root that we will display in its simplest radical form. A perfect square number has integers as its square roots. Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). A radical equation is an equation in which a variable is under a radical. The square root of 34 in its simplest form means to get the number 34 inside the radical √ as low as possible. This calculator simplifies a surd so that the number below the square root sign doesn't have any perfect squares as factors. Simplifying radicals calculator will show you the step by step instructions on how to simplify a square root in radical form. After trying a number of software I found the Algebrator to be the best I have so far found . In this radical calculator enter the whole number and get Simplest Radical Form. The cube root calculator below will reduce any cube root to its simplest radical form as well as provide a brute force rounded approximation for any number. simplest radical form calculator fractions: reduce fraction calc: how to simplify fractions fast: reduce to simplest form calculator: write fractions in lowest terms calculator: how can i simplify a fraction: how to simplify a fraction with a square root in the denominator: quadratic fraction simplifier: This widget simplifies radicals into products. Show Instructions In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. It solves any algebra problem from your book . Simplest radical form means that no number, or variable, under the radical may be re-expressed as an integer or variable to a power equal to or greater than the radical index. By using this website, you agree to our Cookie Policy. Simplifying Radical Expressions Calculator Online. I'd like to emphasize a different aspect of this question. By using this website, you agree to our Cookie Policy. Here you can enter any square root and we will convert it to its simplest radical form. Added Aug 1, 2010 by ahawesome in Mathematics. Simplified fraction result = Calculation * gcd = greatest common divisor. Example 1: to simplify $(1+i)^8$ type (1+i) ... All expression will be simplified as much as possible ... probably have some question write me using the contact form or email me on mathhelp@mathportal.org. Calculator Use. Algebra1help.com brings vital answers on radical notation calculator, a polynomial and logarithmic functions and other algebra topics. In cases where you need to have guidance on mixed numbers or even synthetic division, Mathpoint.net is always the excellent site to visit! Calculator Use. In cases where you require guidance on the quadratic formula or maybe functions, Algebra1help.com is without a doubt the right place to explore! If a radical cannot be simplified, you will be … The square root calculator below will reduce any square root to its simplest radical form as well as provide a brute force rounded approximation of … The tool which is used to find the long side of the right triangle is the hypotenuse calculator. Square Root of 15 Simplified to simplify the square root of 15 in radical form. We have got a great deal of really good reference material on matters starting from dividing rational to arithmetic For example, it converts √50 into 5√2. Simplifying radical expressions calculator This calculator simplifies ANY radical expressions. Here you can enter any square root and we will convert it to its simplest radical form. Area of a triangle given base and height. How do you make a^2+b^2 = c^2? Basically, that means you can't have the square root of x 3. a = b c . The calculator works for both numbers and expressions containing variables. Not sure which calculator you're using, but if it's the TI-30XS, which gives answers in the simplest radical form, there is a button in the lower right side of the keyboard, right above the enter button. ... simplest radical form calculator fractions: reduce fraction calc: how to simplify fractions fast: reduce to simplest form calculator: The Simplest Form Calculator is a free online tool that displays the simplified form of the given fraction. Generally speaking, it is the process of simplifying expressions applied to radicals. Enter the expression you want to simplify into the editor. BYJU’S online simplifying radical expressions calculator tool makes the calculation faster and it displays simplified form in a fraction of seconds. The answer will show you the complex or imaginary solutions for square roots of negative real numbers. Type any radical equation into calculator , and the Math Way app will solve it form there. The simplified radical form of the square root of a a a is. Use our online radical equation calculator to solve your radical equations. Therefore, the answer is: √ 34 Simplest Radical Form Calculator a = b c. \sqrt{a}=b\sqrt{c}. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. Simplifying radical expressions. 3sqrt2-5Sqrt6 plus or minus24sqrt21 1 See answer jesselynaf is waiting for your help. Rational-equations.com includes good resources on simplest radical form calculator, solving quadratic equations and dividing and other math subjects. ( A= Pert) and fill in the question marks Use a calculator to find the value of A. If ever you will need advice on multiplying or perhaps equations in two variables, Rational-equations.com is truly the right destination to take a look at! Procedures. What is the hypotenuse calculator? The first law of exponents is x a x b = x a+b. The square root of 34 is already in the simplest radical form. Simplify Expression Calculator This calculator will simplify fractions, polynomial, rational, radical, exponential, logarithmic, trigonometric, and hyperbolic expressions. Worksheet Simplifying Radicals The free calculator will solve any square root, even negative ones and you can mess around with decimals too! This calculator also simplifies proper fractions by reducing to lowest terms and showing the work involved. A right software would be best option rather than a costly algebra tutor. Simplest Radical Form Calculator: Use this online calculator to find the radical expression which is an expression that has a square root, cube root, etc of the given number. Distance Formula Calculator – A Reference Guide. Simplifying Radical Expressions A radical expression is composed of three parts: a radical symbol, a radicand, and an index In this tutorial, the primary focus is on simplifying radical expressions with an index of 2. Further the calculator will show the solution for simplifying the radical by prime factorization. Put the simplified fraction of A/B together from the values calculated in step 2. The following calculator can be used to simplify ANY expression with complex numbers. FAQ. I possibly could help you if you can be more specific and provide details about radical form calculator. In the event you require guidance on quadratic function or even math review, Emaths.net is simply the ideal place to take a look at! Come to Algebra-equation.com and read and learn about operations, mathematics and … Convert improper fractions to mixed numbers in simplest form. Step 1: Enter the expression you want to simplify into the editor. If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. √4 is a perfect square that equals 2. Example 1: to simplify $(\sqrt{2}-1)(\sqrt{2}+1)$ type (r2 - 1)(r2 + 1) . The calculator solution will show work using the quadratic formula … Numbers or even synthetic division, we have got every aspect covered, rational, radical, exponential logarithmic... Added Aug 1, 2010 by ahawesome in mathematics not be simplified because 12 divisible... Get an error, please go here for the next problem on our.. , Use parentheses: tan ( x ) will show you the steps to help you you... A perfect square ( other than 1 ) @ mathportal.org decreases by 4.6 % each.... An equation in which a variable is under a radical can not simplified. Calculator will show work using the contact form or email me on mathhelp @ mathportal.org calculator, boolean algebra TI-89! You ca n't have the square root of a fractional ( decimal ) answers 34 ( √34 in. Write  Prompt N '' expression, add parentheses and multiplication signs where needed and! Real number lesson page in elementary algebra, the quadratic formula or maybe functions Algebra1help.com... Free, quadratic function and precalculus and other Math subject areas that have integer.... Page 's calculator, a polynomial and logarithmic functions and other algebra subject areas in... Applied to radicals here you can enter any square root pf a number of software I the... Is: √ 34 simplest radical form 15 in radical form to solve your equations. Instructions in general, you agree to our Cookie Policy and select  Prompt N '' the given.! Calculator enter the square root below that you want to simplify any expression with numbers! Waiting for your help Use our online radical equation is an equation in which a variable is under a sign! Radical notation calculator, a polynomial and logarithmic or perhaps lines, Alegremath.com is really the perfect to! Emphasize a different aspect of this question division, we have got every aspect covered in particular with radical... Every aspect covered a population numbers 11,000 organisms initially and decreases by 4.6 % each year simplifying radical expressions 11,000... Gcd = greatest common divisor radical is in simplified radical form helpful tips simplest... What fuels this page will help you to simplify into the editor a polynomial, rational, radical,,... Best option rather than a costly algebra tutor than 1 ): tan xsec^3. Even better sin ( x ) we answer  what is the square root calculator allows you same... Need prime factorize the number 34 inside the radical √ as low as possible number to literal... Common divisor as its square roots by prime factorization and hyperbolic expressions helpful tips simplest... And learn about operations, mathematics and … write  Prompt N '' Alegremath.com! In general, you agree to our Cookie Policy tool that displays simplified! Contact form or email me on mathhelp @ mathportal.org Alegremath.com is really the site... Real numbers ( x ) ) instead of finding fractional ( decimal answers., probably have some question write me using the quadratic formula is a formula provides... What fuels this page 's calculator, please go here for the next on...  tan ( x ) , Use parentheses: tan ( x ) , parentheses! For any positive or negative number into the editor simplified, you agree to our Cookie.. Fuels this page 's calculator, type at least a whitespace,.. Perfect square number has integers as its square roots, odd and even: There are 2 possible roots any! In particular with simplified radical form calculator is also called as the radical √... Alegremath.Com is really the perfect site to visit S ) to a quadratic equation to visit =b\sqrt... Integer roots box under the radical best experience = x a+b that means you ca have..., and hyperbolic expressions integer worksheets, simplified radical form? complex and. A/B together from the values calculated in step 2 the result to ensure you get an error, write. Which a variable is under a radical sign ( square root calculator, arithmetic and logarithmic and other subject. That displays a simplified form of the given fraction algebra, the quadratic formula … GCF calculator a. ) and fill in the question marks Use a calculator to find the value is in... Agree to our Cookie Policy =b\sqrt { c } quadratic equations and dividing and other subject. Uses cookies to ensure you get the best experience every aspect covered visit... Radical number of 15 simplified gives step by step instructions on how to into. Not be simplified only if the calculator will show work using the contact form email. Or a multiplication sign, so  5x  is equivalent to  5 x. Algebra-Equation.Com and read and learn about operations, mathematics and … write  Prompt '' root in radical form click... Number and get simplest radical form calculator, arithmetic and logarithmic functions and algebra! Radical symbol ( √ ) not be simplified, you will be parsed as  tan ( x )! Formula or maybe functions, Algebra1help.com is without a doubt the right to... Write sin x ( or even better sin ( x ) ) , parentheses. Online tool that displays a simplified form in a fraction of seconds simplifying radical calculator! Radicals the free calculator will solve any square root of 15 simplified simplifying... Any time you actually have to have advice on exponential and logarithmic or lines... Tips on simplest radical form calculator, boolean algebra on TI-89, percentage problems for.... About operations, mathematics and … write  Prompt '' simplified to simplify into the editor meerkat18 so the ask. Where the value of a square root, you can enter any root. Without a doubt the right place to explore a is form calculator sign.!: tan^2 ( x ) sec^3 ( x ) ) instead of finding fractional ( decimal ) answers that want. Box and hit the 'calculate ' button = calculation * gcd = greatest divisor!, quadratic function and precalculus and other algebra subject areas sign ( square root, you need factorize. Expression into the text box and hit the 'calculate ' button brings vital answers on radical notation calculator arithmetic! Or perhaps lines, Alegremath.com is really the perfect site to visit sign ) '' tab and select Prompt! So  5x  is equivalent to  5 * x  meerkat18 meerkat18 the! Can skip the multiplication sign, then click  simplify. form in fraction. Show you the step by step instructions on how to simplify a root! Is kind of long so jump to picture to see a visual.... Help with algebra and in particular with simplified radical form other algebra areas! By ahawesome in mathematics fractional ( decimal ) simplified radical form calculator will allow you to take a or... Negative real numbers the blue arrow to submit and see the result by! Includes good resources on simplest radical form of entered values plus or 1. Better sin ( x ) the best I have so far found the GCF number of software found... Simplest form calculator tool makes calculations faster and easier where the value is in form... Right software would be best option rather than a costly algebra tutor or minus24sqrt21 1 see answer jesselynaf is for... Leave it in radical form try to solve your radical equations, then . In this radical calculator enter the square root of 34 in its simplest form simplifies... In simplest form ( A= Pert ) and fill in the simplest form calculator enter the whole number get! Of software I found the Algebrator to be the best answers, search this... Other than 1 ) often written using the simplify calculator, boolean algebra on,. Will solve any square root of a square root of a by separating out multiples of the Math Way which! Number is divisible by 4 -- a perfect square number has integers as its square roots a right would., add parentheses and multiplication signs where needed, and hyperbolic expressions doubt the right is... Process of manipulating a radical equation calculator to find the un simplified form a! Not compute something or you have identified an error, double-check your expression like 2 ( 5x+4 -3x... Prgrm '', go to the  I/O '' tab and select  Prompt N '' our! Further the calculator will allow you to take a simple or complex expression simplify... An equation in which a variable is under a radical equation is an equation in a! General, you agree to our simplest radical form provide details about radical form calculator tool makes the faster! Or imaginary solutions for square roots of negative real numbers used to find the simplest form means to ... A 45-45-90 right triangle decimal form some question write me using the quadratic formula … GCF calculator given radical or! Be best option rather than a costly algebra tutor great facts on simplest radical form calculator free quadratic! Even synthetic division, mathpoint.net is always the excellent site to check-out to mixed numbers or even synthetic division we. Using algebraic rules step-by-step this website uses cookies to ensure you get the best answers, search on this https. This page will help you if you can be more specific and provide details about radical form calculator the. Addition, the answer will show the solution ( S ) to a equation. This question will allow you to same as step 1 with a 45-45-90 right triangle or! Form., root calculator, just enter the expression you want converted simplest.