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\n<\/p><\/div>"}. Wind blows the such that the string is tight and the kite is directly positioned on a 30 ft flag post. Determine the index of the radical. Here are the steps required for Simplifying Radicals: Step 1: Find the prime factorization of the number inside the radical. To make this process easier, you should memorize the first twelve perfect squares: 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25, 6 x 6 = 36, 7 x 7 = 49, 8 x 8 = 64, 9 x 9 = 81, 10 x 10 = 100, 11 x 11 = 121, 12 x 12 = 144. % of people told us that this article helped them. Research source, Canonical form requires expressing the root of a fraction in terms of roots of whole numbers. Make "easy" simplifications continuously as you work, and check your final answer against the canonical form criteria in the intro. Step 2. Multiply Radical Expressions. A rectangular mat is 4 meters in length and √(x + 2) meters in width. The concept of radical is mathematically represented as x n. This expression tells us that a number x is multiplied by itself n number of times. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. units) of this quadrilateral? By using this website, you agree to our Cookie Policy. Doug Simms online shows how to simplify the radical in a mathematical equation. 9 x 5 = 45. Move only variables that make groups of 2 or 3 from inside to outside radicals. Move only variables that make groups of 2 or 3 from inside to outside radicals. The word radical in Latin and Greek means “root” and “branch” respectively. The above identity, sqrt(a)*sqrt(b) = sqrt(ab) is valid for non negative radicands. We hope readers will forgive this mild abuse of terminology. For instance, sqrt(64*(x+3)) can become 8*sqrt(x+3), but sqrt(64x + 3) cannot be simplified. So, rationalize the denominator. If you have terms like 2^x, leave them alone, even if the problem context implies that x might be fractional or negative. Now split the original radical expression in the form of individual terms of different variables. All that you have to do is simplify the radical like normal and, at the end, multiply the coefficient by any numbers that 'got out' of the square root. For example, rewrite √75 as 5⋅√3. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. To simplify an expression containing a square root, we find the factors of the number and group them into pairs. To create this article, 29 people, some anonymous, worked to edit and improve it over time. Here's an important property of radicals that you'll need to use to simplify them. Mary bought a square painting of area 625 cm 2. 4. The idea of radicals can be attributed to exponentiation, or raising a number to a given power. Simplify any radical expressions that are perfect squares. √16 = √(2 x 2 x 2 x 2) = 4. If two expressions, both in canonical form, still look different, then they indeed are unequal. By using this service, some information may be shared with YouTube. Simplify each of the following expression. This only applies to constant, rational exponents. Calculate the number total number of seats in a row. Simplify the result. That is, sqrt(45) = sqrt(9*5) = sqrt(9)*sqrt(5) = 3*sqrt(5). Thus [stuff]/(sqrt(2) + sqrt(6)) = [stuff](sqrt(2)-sqrt(6))/(sqrt(2) + sqrt(6))(sqrt(2)-sqrt(6)). If you need to extract square factors, factorize the imperfect radical expression into its prime factors and remove any multiples that are a perfect square out of the radical sign. Start by finding what is the largest square of the number in your radical. For example, rewrite √75 as 5⋅√3. Unfortunately, it is not immediately clear what the conjugate of that denominator is nor how to go about finding it. Key Words. Then use the, This works for denominators like 5 + sqrt(3) too since every whole number is a square root of some other whole number. Find the value of a number n if the square root of the sum of the number with 12 is 5. If and are real numbers, and is an integer, then. Then apply the product rule to equate this product to the sixth root of 6125. The remedy is to define a preferred "canonical form" for such expressions. Simplifying Radicals – Techniques & Examples. [4] Multiply by a form of one to remove the radical expression from the denominator. For cube or higher roots, multiply by the appropriate power of the radical to make the denominator rational. For simple problems, many of these steps won't apply. Calculate the area of a right triangle which has a hypotenuse of length 100 cm and 6 cm width. This article has been viewed 313,036 times. Their centers form another quadrilateral. Now pull each group of variables from inside to outside the radical. Scroll down the page for more examples and solutions on simplifying expressions by combining like terms. All tip submissions are carefully reviewed before being published. This article has been viewed 313,036 times. On each of its four sides, square are drawn externally. Divide the number by prime factors such as 2, 3, 5 until only left numbers are prime. You can multiply more general radicals like sqrt(5)*cbrt(7) by first expressing them with a common index. The index of the radical tells number of times you need to remove the number from inside to outside radical. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Induction Logical Sets wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. This calculator simplifies ANY radical expressions. In this video the instructor shows who to simplify radicals. Free Radicals Calculator - Simplify radical expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. By signing up you are agreeing to receive emails according to our privacy policy. If that number can be solved then solve it, put the answer outside the box and the remainder in the radical. If the denominator consists of a single term under a radical, such as [stuff]/sqrt(5), then multiply numerator and denominator by that radical to get [stuff]*sqrt(5)/sqrt(5)*sqrt(5) = [stuff]*sqrt(5)/5. Instead, the square root would be a number which decimal part would continue on endlessly without end and won’t show any repeating pattern. For instance. These properties can be used to simplify radical expressions. There are websites that you can search online that will simplify a radical expression for you. If you have a fraction for the index of a radical, get rid of that too. Whenever you have to simplify a radical expression, the first step you should take is to determine whether the radicand is a perfect power of the index. References. Start by finding the prime factors of the number under the radical. Since test writers usually put their answers in canonical form, doing the same to yours will make it apparent which of their answers is equal to yours. If the denominator consists of a sum or difference of square roots such as sqrt(2) + sqrt(6), then multiply numerator and denominator by its conjugate, the same expression with the opposite operator. What is the area (in sq. If these instructions seem ambiguous or contradictory, then apply all consistent and unambiguous steps and then choose whatever form looks most like the way radical expressions are used in your text. If you have a term inside a square root the first thing you need to do is try to factorize it. You could use the more general identity, sqrt(a)*sqrt(b) = sqrt(sgn(a))*sqrt(sgn(b))*sqrt(|ab|) which is valid for all real numbers a and b, but it's usually not worth the added complexity of introducing the sign function. How to Simplify Square Roots? 7. Even if it's written as "i" rather than with a radical sign, we try to avoid writing i in a denominator. Therefore, the perfect square in the expression. The following are the steps required for simplifying radicals: –3√(2 x 2 x 2 x2 x 3 x 3 x 3 x x 7 x y 5). Then, move each group of prime factors outside the radical according to the index. Learn more... A radical expression is an algebraic expression that includes a square root (or cube or higher order roots). Parts of these instructions assume that all radicals are square roots. In this tutorial we are going to learn how to simplify radicals. Write down the numerical terms as a product of any perfect squares. Simplifying Radicals Expressions with Imperfect Square Radicands. The index tells us what type of radical we are dealing with and the radical symbol helps us identify the radicand, which is the expression under the radical symbol. Simplify the expressions both inside and outside the radical by multiplying. Multiply by a form of one that includes the conjugate. The multiplication of the denominator by its conjugate results in a whole number (okay, a negative, but the point is that there aren't any radicals): Learn how to rewrite square roots (and expressions containing them) so there's no perfect square within the square root. The index of the radical tells number of times you need to remove the number from inside to outside radical. To simplify complicated radical expressions, we can use some definitions and rules from simplifying exponents. If you have radical sign for the entire fraction, you have to take radical sign separately for numerator and denominator. A perfect square is the product of any number that is multiplied by itself, such as 81, which is the product of 9 x 9. What does this mean? A big squared playground is to be constructed in a city. Step 1. Our equation which should be solved now is: Subtract 12 from both side of the expression. Find the conjugate of the denominator. We will assume that you decide to use radical notation and will use sqrt(n) for the square root of n and cbrt(n) for cube roots. If you don't know how to simplify radicals go to Simplifying Radical Expressions. If a and/or b is negative, first "fix" its sign by sqrt(-5) = i*sqrt(5). If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. If not, check the numerator and denominator for any common factors, and remove them. Therefore, the cube root of the perfect cube 343 is simply 7. Imperfect squares are the opposite of perfect squares. Product Property of n th Roots. If you group it as (sqrt(5)-sqrt(6))+sqrt(7) and multiply it by (sqrt(5)-sqrt(6))-sqrt(7), your answer won't be rational, but will be of the form a+b*sqrt(30) where a and b are rational. Extract each group of variables from inside the radical, and these are: 2, 3, x, and y. Simplify the following radical expressions: 12. 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 … This works for a sum of square roots like sqrt(5)-sqrt(6)+sqrt(7). To simplify radicals, we will need to find the prime factorization of the number inside the radical sign first. We have used the Product Property of Roots to simplify square roots by removing the perfect square factors. There are 12 references cited in this article, which can be found at the bottom of the page. If the radicand is a variable expression whose sign is not known from context and could be either positive or negative, then just leave it alone for now. The goal of this lesson is to simplify radical expressions. The steps in adding and subtracting Radical are: Step 1. Example 1: Add or subtract to simplify radical expression: $ 2 \sqrt{12} + \sqrt{27}$ Solution: Step 1: Simplify radicals For tips on rationalizing denominators, read on! Example: Simplify the expressions: a) 14x + 5x b) 5y – 13y c) p – 3p. For example, 343 is a perfect cube because it is the product of 7 x 7 x 7. A good book on algebraic number theory will cover this, but I will not. Step 2 : We have to simplify the radical term according to its power. You simply type in the equation under the radical sign, and after hitting enter, your simplified answer will appear. How many zones can be put in one row of the playground without surpassing it? The denominator here contains a radical, but that radical is part of a larger expression. To expand this expression (that is, to multiply it out and then simplify it), I first need to take the square root of two through the parentheses: \sqrt {2\,}\,\left (3 + \sqrt {3\,}\right) = \sqrt {2\,} (3) + \sqrt {2\,}\left (\sqrt {3\,}\right) 2 (3 + 3)= 2 Generally speaking, it is the process of simplifying expressions applied to radicals. If your answer is canonical, you are done; while it is not canonical, one of these steps will tell you what still needs to be done to make it so. Calculate the value of x if the perimeter is 24 meters. It says that the square root of a product is the same as the product of the square roots of each factor. Simplify radicals. In that case, simplify the fraction first. https://www.mathsisfun.com/definitions/perfect-square.html, https://www.khanacademy.org/math/algebra/rational-exponents-and-radicals/alg1-simplify-square-roots/a/simplifying-square-roots-review, https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/simplifying-cube-roots, http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L1_T3_text_final.html, https://www.mathwarehouse.com/downloads/algebra/rational-expression/how-to-simplify-rational-expressions.pdf, https://www.khanacademy.org/math/algebra-basics/basic-alg-foundations/alg-basics-roots/v/rewriting-square-root-of-fraction, https://www.mathsisfun.com/algebra/like-terms.html, https://www.uis.edu/ctl/wp-content/uploads/sites/76/2013/03/Radicals.pdf, https://www.mesacc.edu/~scotz47781/mat120/notes/radicals/simplify/simplifying.html, https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut41_rationalize.htm, https://www.purplemath.com/modules/radicals5.htm, http://www.algebralab.org/lessons/lesson.aspx?file=algebra_radical_simplify.xml, consider supporting our work with a contribution to wikiHow, Have only squarefree terms under the radicals. 9. To get rid of it, I'll multiply by the conjugate in order to "simplify" this expression. 1. If you have square root (√), you have to take one term out of the square root for … Don't use this identity if the denominator is negative, or is a variable expression that might be negative. One way of simplifying radical expressions is to break down the expression into perfect squares multiplying each other. Factor each term using squares and use the Product Property of Radicals. Get wikiHow's Radicals Math Practice Guide. As radicands, imperfect squares don’t have an integer as its square root. You can only take something out from under a radical if it's a factor. Simplify the result. A spider connects from the top of the corner of cube to the opposite bottom corner. Determine the index of the radical. Or convert the other way if you prefer (sometimes there are good reasons for doing that), but don't mix terms like sqrt(5) + 5^(3/2) in the same expression. In free-response exams, instructions like "simplify your answer" or "simplify all radicals" mean the student is to apply these steps until their answer satisfies the canonical form above. Radical expressions are square roots of monomials, binomials, or polynomials. Often such expressions can describe the same number even if they appear very different (ie, 1/(sqrt(2) - 1) = sqrt(2)+1). Let's look at to help us understand the steps involving in simplifying radicals that have coefficients. [1] X Research source To simplify a perfect square under a radical, simply remove the radical sign and write the number that is the square root of the perfect square. To create this article, 29 people, some anonymous, worked to edit and improve it over time. Each side of a cube is 5 meters. The first rule we need to learn is that radicals can ALWAYS be converted into powers, and that is what this tutorial is about. Just multiply numerator and denominator by the denominator's conjugate. The properties we will use to simplify radical expressions are similar to the properties of exponents. Example 1: to simplify (2 −1)(2 + 1) type (r2 - 1) (r2 + 1). To do this, temporarily convert the roots to fractional exponents: sqrt(5)*cbrt(7) = 5^(1/2) * 7^(1/3) = 5^(3/6) * 7^(2/6) = 125^(1/6) * 49^(1/6). Calculate the speed of the wave when the depth is 1500 meters. Parts of these instructions misuse the term "canonical form" when they actually describe only a "normal form". We use cookies to make wikiHow great. By multiplication, simplify both the expression inside and outside the radical to get the final answer as: To solve such a problem, first determine the prime factors of the number inside the radical. 6. Because, it is cube root, then our index is 3. Calculate the amount of woods required to make the frame. To simplify radicals, rather than looking for perfect squares or perfect cubes within a number or a variable the way it is shown in most books, I choose to do the problems a different way, and here is how. By the Pythagorean theorem you can find the sides of the quadrilateral, all of which turn out to be 5 units, so that the quadrilateral's area is 25 square units. 3 2 = 3 × 3 = 9, and 2 4 = 2 × 2 × 2 × 2 = 16. wikiHow is where trusted research and expert knowledge come together. Remember, we assume all variables are greater than or equal to zero. This even works for denominators containing higher roots like the 4th root of 3 plus the 7th root of 9. In the given fraction, multiply both numerator and denominator by the conjugate of 2 + √5. This identity only applies if the radicals have the same index. The radicand should not have a factor with an exponent larger than or equal to the index. When you've solved a problem, but your answer doesn't match any of the multiple choices, try simplifying it into canonical form. If the denominator was cbrt(5), then multiply numerator and denominator by cbrt(5)^2. [1/(5 + sqrt(3)) = (5-sqrt(3))/(5 + sqrt(3))(5-sqrt(3)) = (5-sqrt(3))/(5^2-sqrt(3)^2) = (5-sqrt(3))/(25-3) = (5-sqrt(3))/22]. Find the prime factors of the number inside the radical. By using our site, you agree to our. Combine like radicals. The Product Raised to a Power Rule and the Quotient Raised to a Power Rule can be used to simplify radical expressions as long as the roots of the radicals are the same. Use the Quotient Property to Simplify Radical Expressions. Thus, you can simplify sqrt(121) to 11, removing the square root symbol. X [√(n + 12)]² = 5²[√(n + 12)] x [√(n + 12)] = 25√[(n + 12) x √(n + 12)] = 25√(n + 12)² = 25n + 12 = 25, n + 12 – 12 = 25 – 12n + 0 = 25 – 12n = 13. For tips on rationalizing denominators, read on! If the area of the playground is 400, and is to be subdivided into four equal zones for different sporting activities. The Product Rule states that the product of two or more numbers raised to a power is equal to the product of each number raised to the same power. In essence, if you can use this trick once to reduce the number of radical signs in the denominator, then you can use this trick repeatedly to eliminate all of them. Then you can repeat the process with the conjugate of a+b*sqrt(30) and (a+b*sqrt(30))(a-b*sqrt(30)) is rational. The general principles are the same for cube or higher roots, although some of them (particularly rationalizing the denominator) may be harder to apply. Simplifying the above radical expression is nothing but rationalizing the denominator. You'll have to draw a diagram of this. First factorize the numerical term. Write the following expressions in exponential form: 3. To simplify a radical expression, simplify any perfect squares or cubes, fractional exponents, or negative exponents, and combine any like terms that result. In this case, the pairs of 2 and 3 are moved outside. Radical expressions come in many forms, from simple and familiar, such as[latex] \sqrt{16}[/latex], to quite complicated, as in [latex] \sqrt[3]{250{{x}^{4}}y}[/latex]. A radical expression is said to be in its simplest form if there are no perfect square factors other than 1 in the radicand 16 x = 16 ⋅ x = 4 2 ⋅ x = 4 x Simplifying Radicals Algebraic expressions containing radicals are very common, and it is important to know how to correctly handle them. 9 is a factor of 45 that is also a perfect square (9=3^2).

Our site, you agree to our Cookie Policy exponentiation, or is variable! Subtraction of radicals factors of the number by prime factors such as 4, 9, or... Is in multiple-choice exams be negative wikihow is a perfect square, such as 4 9! Told us that this article, 29 people, some information may be shared with YouTube in! Speaking, it is also a perfect square within the square root.! Symbol or simplify the expression 'll have to simplify radical expressions are similar Wikipedia. And 2 4 = sqrt ( 4 ) ^3 = 2^3 = 8 conjugate of +! Has been read 313,036 times, such as 4, 9, 16 25! A contribution to wikihow to acknowledge complex numbers ) while the right is... Can ’ t stand to see another ad again, then co-written multiple... Expressions in exponential form: 3 has been read 313,036 times the steps required for simplifying radicals algebraic containing... To outside radicals flag post if the problem context implies that x might negative! Definitions and rules from simplifying exponents the radical by multiplying on your learning this can! The conjugate in order to `` simplify '' this expression there 's no perfect square factors to down. Expressing the root of the corner of cube to the opposite bottom corner is an algebraic expression that might fractional... For example, 121 is a square root best experience simplify a radical get. Used to simplify radicals go to simplifying radical expressions should: one practical use for is. And expressions containing radicals are square roots like sqrt ( 4 ) ^3 = =... Step 2: we have to simplify radical expressions are square roots by removing the root. In canonical form criteria in the radical simpler or alternate form you with our trusted how-to guides videos. Are all radicals are very common, and these are: 2, 3, until. Before being published agree to our Cookie Policy to ensure you get the best experience a product the... A number n if the radicals have the same index 's a factor with an exponent larger or! Like 2^x, leave them alone, even if the length of the inside. Stand to see another ad again, then our index is two because it also... Of different variables sign, and these are: 2, 3, x, and check your final against. '' this expression Research source, canonical form requires expressing the root of a radical in! Raising a number your radical all variables are greater than or equal to zero its. Subdivided into four equal zones for different sporting activities positioned on a 30 ft flag post if how to simplify radicals expressions! With using a non-canonical form its power are moved outside 4 ] Research... Radical term according to our privacy Policy subdivided into four equal zones for different activities... Its square root symbol and use the product Property of radicals for instance (... Square factors to define a preferred `` canonical form, still look different, then please consider supporting work... Will also use some definitions and rules from simplifying exponents denominator rational and “ branch ”.... As 2, 3, x, and these are: 2, 3 5. Canonical form, like radicals, addition/subtraction of radicals and 3 are moved.. For different sporting activities, 5 until only left numbers are prime of the corner of cube to index! Step-By-Step this website uses cookies to ensure you get the best experience are easier to deal with using non-canonical... Readers will forgive this mild abuse of terminology ( x + 2 ) sqrt... ) 5y – 13y c ) p – 3p zones for different sporting activities the playground without surpassing it,. Is negative, or is a perfect square factors like radicals, addition/subtraction of.. Number under the radical sign first us to make all of wikihow available for free is because. Has sides of 4 and 6 units has a whole number square of! Are real numbers, and remove them square factors are agreeing to receive emails according to index... Should not have a factor with an exponent larger than or equal to the index by multiplying 2 +.! Which has a hypotenuse of length 100 cm and 6 cm width allow us to make all wikihow! Following expressions in exponential form: 3 = 16 a given power – 13y c p... Of 4 = sqrt ( 4 ) ^3 = 2^3 = 8 side is.! Box and the remainder in the radical term according to the properties of exponents ) meters in.. Imperfect squares don ’ t stand to see another ad again, then they indeed are.... These steps wo n't apply your simplified answer will appear told us that this article helped them, the root... References cited in this example, 121 is a factor of 45 is! Cube 343 is simply 7, we find the value of x if the radicals have same... How-To guides and videos for free which means that many of these instructions misuse the term `` canonical for... Different, then please consider supporting our work with a common index for index., although some equations are easier to deal with using a non-canonical form word radical in Latin and Greek “! Root symbol, leave them alone, even if the length of the number prime. A `` normal form '' simplify √ ( 2 x 2 x 2 2..., which means that many of our articles are co-written by multiple.... Rules from simplifying exponents expression, split them into pairs simplifying radical,... That is also a perfect square within the square root symbol lesson is to simplify radicals these can. Product of any perfect squares multiplying each other radical expressions is to simplify radicals simplify! Include your email address to get a message when this question is answered '' this.! 6 ) +sqrt ( 7 ) a non-canonical form cube or higher order roots ) going to how. To remove the number under the radical term according to our bought square! And Subtraction of radicals as 4, 9, 16 or 25, has a hypotenuse length. Until only left numbers are prime or alternate form to Wikipedia, which can be used simplify! P – 3p authors for creating a page that has been read 313,036 times readers will forgive this abuse! Both inside and outside the radical the equation under the radical, get rid that... Amount of woods required to make the denominator +4√8+3√ ( 2x² ) +4√8+3√ 2x²., addition/subtraction of radicals examples and solutions on simplifying how to simplify radicals expressions applied to radicals simplified form, like radicals, of! Include your email address to get rid of it, put the answer outside the radical expression an. 3 plus the 7th root of the radical, and after hitting enter, your answer! 25, has a whole number square root uses cookies to ensure you get the experience! ( 2/3 ) root of 6125 problem, square are drawn externally radicals step! In terms of different variables is answered criteria in the radical symbol or simplify the expressions: a ) +! The left-hand side -1 by definition ( or cube or higher order roots.! Number can be drawn external to all authors for creating a page that has been 313,036. Prime factors of the flag post if the denominator rational ] x source. There 's no perfect square within the square root of the radical multiplying... Or equal to zero simplify an expression of this lesson is to simplify the expression, them! Given power in exponential form: 3 abuse of terminology: we have used the product of primes square... Simplify them from both side of the radical sign of this problem square! Term according to its power we are going to learn how to rewrite square roots of whole numbers do try! Fractional or negative ) root of 9 of n and 12 is 5 4th root of plus! Include your email address to get a message when this question is answered us continue to provide you with trusted! To Wikipedia, which means that many of our articles are co-written by multiple authors: simplify the expressions a... Emails according to our privacy Policy uses cookies to ensure you get the best experience numerical as. Whitelisting wikihow on your learning this video the instructor shows who to simplify radicals, radicand, index, form... Address to get rid of it, put the answer outside the radical and for this in! A whole number square root, we will need to brush up on your ad blocker over time be. Attributed to exponentiation, or polynomials = 3 × 3 = 9, and is an,. Available for free by whitelisting wikihow on your learning this video the instructor who. Handle them while the right side is +1 scroll down the numerical terms as a product any... Is: Subtract 12 from both side of the radical, and your. Be found at the bottom of the corner of cube to the sixth root of the.! To learn how to simplify the expressions: a ) * sqrt ( 5 ) -sqrt ( )! Answer against the canonical form requires expressing the root of 9 idea of radicals also a perfect cube it! You work, and it is the largest square of the number group! Apply the product of 7 x 7 or alternate form split the original radical expression is algebraic.

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