We use cookies to give you the best experience on our website. Determine the index of the radical. A perfect square is the … The solution to this problem should look something like this…. If you're behind a web filter, … ... A worked example of simplifying an expression that is a sum of several radicals. Generally speaking, it is the process of simplifying expressions applied to radicals. You just need to make sure that you further simplify the leftover radicand (stuff inside the radical symbol). Find the largest perfect square that is a factor of the radicand (just like before) 4 is the largest perfect square that is a factor of 8. (When moving the terms, we must remember to move the + or – attached in front of them). And it checks when solved in the calculator. Each side of a cube is 5 meters. Example 3: Simplify the radical expression \sqrt {72} . Let’s deal with them separately. Remember that getting the square root of “something” is equivalent to raising that “something” to a fractional exponent of {1 \over 2}. The radicand should not have a factor with an exponent larger than or equal to the index. Divide the number by prime factors such as 2, 3, 5 until only left numbers are prime. A spider connects from the top of the corner of cube to the opposite bottom corner. Example 1: to simplify $(\sqrt{2}-1)(\sqrt{2}+1)$ type (r2 - 1)(r2 + 1). . The paired prime numbers will get out of the square root symbol, while the single prime will stay inside. Example 12: Simplify the radical expression \sqrt {125} . Find the index of the radical and for this case, our index is two because it is a square root. Our equation which should be solved now is: Subtract 12 from both side of the expression. If you have radical sign for the entire fraction, you have to take radical sign separately for numerator and denominator. So, , and so on. Example 4 – Simplify: Step 1: Find the prime factorization of the number inside the radical and factor each variable inside the radical. Simplify each of the following expression. If we do have a radical sign, we have to rationalize the denominator. 1. Wind blows the such that the string is tight and the kite is directly positioned on a 30 ft flag post. • Simplify complex rational expressions that involve sums or di ff erences … So we expect that the square root of 60 must contain decimal values. 10. An expression is considered simplified only if there is no radical sign in the denominator. If you're seeing this message, it means we're having trouble loading external resources on our website. For the number in the radicand, I see that 400 = 202. Simplify the following radical expressions: 12. The formula for calculating the speed of a wave is given as , V=√9.8d, where d is the depth of the ocean in meters. A radical expression is composed of three parts: a radical symbol, a radicand, and an index. 6. So which one should I pick? Then express the prime numbers in pairs as much as possible. Simplifying Radicals Operations with Radicals 2. Simplifying Radical Expressions Radical expressions are square roots of monomials, binomials, or polynomials. Let’s find a perfect square factor for the radicand. 27. 5. Now pull each group of variables from inside to outside the radical. For instance, x2 is a p… Simplify. Square root, cube root, forth root are all radicals. However, I hope you can see that by doing some rearrangement to the terms that it matches with our final answer. A kite is secured tied on a ground by a string. $1 per month helps!! For the numerical term 12, its largest perfect square factor is 4. Example 2: Simplify the radical expression \sqrt {60}. 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. Solution: a) 14x + 5x = (14 + 5)x = 19x b) 5y – 13y = (5 –13)y = –8y c) p – 3p = (1 – 3)p = – 2p. 1. What rule did I use to break them as a product of square roots? One way to think about it, a pair of any number is a perfect square! Express the odd powers as even numbers plus 1 then apply the square root to simplify further. 5. Write the following expressions in exponential form: 2. Example 1: Simplify the radical expression. Examples C) If n is an ODD positive integer then Examples Questions With Answers Rewrite, if possible, the following expressions without radicals (simplify) Solutions to the Above Problems The index of the radical 3 is odd and equal to the power of the radicand. Step 2 : We have to simplify the radical term according to its power. Calculate the area of a right triangle which has a hypotenuse of length 100 cm and 6 cm width. Fantastic! Move only variables that make groups of 2 or 3 from inside to outside radicals. Similar radicals. Solving Radical Equations Pull terms out from under the radical, assuming positive real numbers. Because, it is cube root, then our index is 3. Add and Subtract Radical Expressions. since √x is a real number, x is positive and therefore |x| = x. is not a real number since -x 2 - 1 is always negative. Notice that the square root of each number above yields a whole number answer. Examples of How to Simplify Radical Expressions. Raise to the power of . 4. For example, in not in simplified form. The number 16 is obviously a perfect square because I can find a whole number that when multiplied by itself gives the target number. √12 = √ (2 ⋅ 2 ⋅ 3) = 2√3. Example 4: Simplify the radical expression \sqrt {48} . RATIONAL EXPRESSIONS Rational Expressions After completing this section, students should be able to: • Simplify rational expressions by factoring and cancelling common factors. See below 2 examples of radical expressions. Fractional radicand . Going through some of the squares of the natural numbers…. You da real mvps! Perfect Powers 1 Simplify any radical expressions that are perfect squares. The number 16 is obviously a perfect square because I can find a whole number that when multiplied by itself gives the target number. Thus, the answer is. This is achieved by multiplying both the numerator and denominator by the radical in the denominator. Rewrite as . Remember, the square root of perfect squares comes out very nicely! Perfect cubes include: 1, 8, 27, 64, etc. One method of simplifying this expression is to factor and pull out groups of a 3, as shown below in this example. Example 10: Simplify the radical expression \sqrt {147{w^6}{q^7}{r^{27}}}. • Add and subtract rational expressions. 1 6. A radical expression is a numerical expression or an algebraic expression that include a radical. Multiply the numbers inside the radical signs. My apologies in advance, I kept saying rational when I meant to say radical. For this problem, we are going to solve it in two ways. Calculate the amount of woods required to make the frame. Example 11: Simplify the radical expression \sqrt {32} . 2 1) a a= b) a2 ba= × 3) a b b a = 4. To simplify this radical number, try factoring it out such that one of the factors is a perfect square. This is an easy one! Multiply by . Use the power rule to combine exponents. 3 2 = 3 × 3 = 9, and 2 4 = 2 × 2 × 2 × 2 = 16. In this last video, we show more examples of simplifying a quotient with radicals. If the term has an even power already, then you have nothing to do. Example 14: Simplify the radical expression \sqrt {18m{}^{11}{n^{12}}{k^{13}}}. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. These properties can be used to simplify radical expressions. The calculator presents the answer a little bit different. However, the key concept is there. Simplify. Sometimes radical expressions can be simplified. 11. However, the best option is the largest possible one because this greatly reduces the number of steps in the solution. Examples Rationalize and simplify the given expressions Answers to the above examples 1) Write 128 and 32 as product/powers of prime factors: … Rationalizing the Denominator. For example the perfect squares are: 1, 4, 9, 16, 25, 36, etc., because 1 = 12, 4 = 22, 9 = 32, 16 = 42, 25 = 52, 36 = 62, and so on. Multiply the variables both outside and inside the radical. In this case, the pairs of 2 and 3 are moved outside. A school auditorium has 3136 total number of seats, if the number of seats in the row is equal to the number of seats in the columns. Rewrite 4 4 as 22 2 2. Example 4 : Simplify the radical expression : √243 - 5√12 + √27. Think of them as perfectly well-behaved numbers. √27 = √ (3 ⋅ 3 ⋅ 3) = 3√3. The radicand contains both numbers and variables. \(\sqrt{15}\) B. We hope that some of those pieces can be further simplified because the radicands (stuff inside the symbol) are perfect squares. Or you could start looking at perfect square and see if you recognize any of them as factors. Calculate the speed of the wave when the depth is 1500 meters. Combine and simplify the denominator. In this example, we simplify √(2x²)+4√8+3√(2x²)+√8. Simply put, divide the exponent of that “something” by 2. Adding and Subtracting Radical Expressions, That’s the reason why we want to express them with even powers since. √243 = √ (3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3) = 9√3. After doing some trial and error, I found out that any of the perfect squares 4, 9 and 36 can divide 72. Example 7: Simplify the radical expression \sqrt {12{x^2}{y^4}} . Mary bought a square painting of area 625 cm 2. You could start by doing a factor tree and find all the prime factors. √4 4. Let’s do that by going over concrete examples. Step-by-Step Examples. If you have square root (√), you have to take one term out of the square root for every two same terms multiplied inside the radical. Radicals, radicand, index, simplified form, like radicals, addition/subtraction of radicals. Radical Expressions and Equations. Therefore, we have √1 = 1, √4 = 2, √9= 3, etc. Example 9: Simplify the radical expression \sqrt {400{h^3}{k^9}{m^7}{n^{13}}} . A rectangular mat is 4 meters in length and √(x + 2) meters in width. There should be no fraction in the radicand. More so, the variable expressions above are also perfect squares because all variables have even exponents or powers. Example 5: Simplify the radical expression \sqrt {200} . The idea of radicals can be attributed to exponentiation, or raising a number to a given power. Start by finding the prime factors of the number under the radical. Step 1. The main approach is to express each variable as a product of terms with even and odd exponents. Here’s a radical expression that needs simplifying, . It must be 4 since (4)(4) =  42 = 16. Simplifying the square roots of powers. Example: Simplify … You will see that for bigger powers, this method can be tedious and time-consuming. 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. A radical expression is said to be in its simplest form if there are. 2nd level. Enter YOUR Problem. For example, the sum of \(\sqrt{2}\) and \(3\sqrt{2}\) is \(4\sqrt{2}\). Variables with exponents also count as perfect powers if the exponent is a multiple of the index. Here it is! Please click OK or SCROLL DOWN to use this site with cookies. 7. √x2 + 5 and 10 5√32 x 2 + 5 a n d 10 32 5 Notice also that radical expressions can also have fractions as expressions. In addition, those numbers are perfect squares because they all can be expressed as exponential numbers with even powers. Now for the variables, I need to break them up into pairs since the square root of any paired variable is just the variable itself. Simplify by multiplication of all variables both inside and outside the radical. Next, express the radicand as products of square roots, and simplify. 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). 4 = 4 2, which means that the square root of \color{blue}16 is just a whole number. How many zones can be put in one row of the playground without surpassing it? Radical expressions are expressions that contain radicals. no perfect square factors other than 1 in the radicand $$\sqrt{16x}=\sqrt{16}\cdot \sqrt{x}=\sqrt{4^{2}}\cdot \sqrt{x}=4\sqrt{x}$$ no fractions in the radicand and The goal of this lesson is to simplify radical expressions. Compare what happens if I simplify the radical expression using each of the three possible perfect square factors. Otherwise, you need to express it as some even power plus 1. Calculate the number total number of seats in a row. Let’s explore some radical expressions now and see how to simplify them. Example 1. For example ; Since the index is understood to be 2, a pair of 2s can move out, a pair of xs can move out and a pair of ys can move out. How to Simplify Radicals? Calculate the value of x if the perimeter is 24 meters. The answer must be some number n found between 7 and 8. You can do some trial and error to find a number when squared gives 60. One way of simplifying radical expressions is to break down the expression into perfect squares multiplying each other. In order to simplify radical expressions, you need to be aware of the following rules and properties of radicals 1) From definition of n th root(s) and principal root Examples ... More examples on how to Rationalize Denominators of Radical Expressions. A worked example of simplifying an expression that is a sum of several radicals. A radical expression is any mathematical expression containing a radical symbol (√). We can add or subtract radical expressions only when they have the same radicand and when they have the same radical type such as square roots. 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. Add and . Therefore, we need two of a kind. Raise to the power of . . Example 2: Simplify by multiplying. The powers don’t need to be “2” all the time. It’s okay if ever you start with the smaller perfect square factors. Note, for each pair, only one shows on the outside. “Division of Even Powers” Method: You can’t find this name in any algebra textbook because I made it up. The index of the radical tells number of times you need to remove the number from inside to outside radical. Multiplication of Radicals Simplifying Radical Expressions Example 3: \(\sqrt{3} \times \sqrt{5} = ?\) A. [√(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. 3. \sqrt {16} 16. . Find the value of a number n if the square root of the sum of the number with 12 is 5. Actually, any of the three perfect square factors should work. Pairing Method: This is the usual way where we group the variables into two and then apply the square root operation to take the variable outside the radical symbol. Example 1: Simplify the radical expression \sqrt {16} . A rectangular mat is 4 meters in length and √ (x + 2) meters in width. Extract each group of variables from inside the radical, and these are: 2, 3, x, and y. Below is a screenshot of the answer from the calculator which verifies our answer. Then put this result inside a radical symbol for your answer. This is an easy one! \(\sqrt{8}\) C. \(3\sqrt{5}\) D. \(5\sqrt{3}\) E. \(\sqrt{-1}\) Answer: The correct answer is A. Radical Expressions and Equations. Example: Simplify the expressions: a) 14x + 5x b) 5y – 13y c) p – 3p. In this tutorial, the primary focus is on simplifying radical expressions with an index of 2. However, it is often possible to simplify radical expressions, and that may change the radicand. Examples There are a couple different ways to simplify this radical. As you become more familiar with dividing and simplifying radical expressions, make sure you continue to pay attention to the roots of the radicals that you are dividing. Although 25 can divide 200, the largest one is 100. Rewrite the radical as a product of the square root of 4 (found in last step) and its matching factor(2) The standard way of writing the final answer is to place all the terms (both numbers and variables) that are outside the radical symbol in front of the terms that remain inside. If the area of the playground is 400, and is to be subdivided into four equal zones for different sporting activities. Rewrite as . Starting with a single radical expression, we want to break it down into pieces of “smaller” radical expressions. To simplify an algebraic expression that consists of both like and unlike terms, it might be helpful to first move the like terms together. Remember the rule below as you will use this over and over again. Example 13: Simplify the radical expression \sqrt {80{x^3}y\,{z^5}}. Adding and … Find the height of the flag post if the length of the string is 110 ft long. Simplifying radicals is the process of manipulating a radical expression into a simpler or alternate form. Looks like the calculator agrees with our answer. The word radical in Latin and Greek means “root” and “branch” respectively. For instance. Step 2. Simplest form. 4. 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]. Roots and radical expressions 1. Adding and Subtracting Radical Expressions 2 2. Simplify the following radicals. Calculate the value of x if the perimeter is 24 meters. Repeat the process until such time when the radicand no longer has a perfect square factor. Solution : Decompose 243, 12 and 27 into prime factors using synthetic division. :) https://www.patreon.com/patrickjmt !! Write the following expressions in exponential form: 3. Multiply and . • Multiply and divide rational expressions. Multiplying Radical Expressions SIMPLIFYING RADICALS. √22 2 2. To simplify complicated radical expressions, we can use some definitions and rules from simplifying exponents. Simplifying Radicals – Techniques & Examples. A radical can be defined as a symbol that indicate the root of a number. Otherwise, check your browser settings to turn cookies off or discontinue using the site. Algebra. Example 8: Simplify the radical expression \sqrt {54{a^{10}}{b^{16}}{c^7}}. This type of radical is commonly known as the square root. What does this mean? Simplifying Radical Expressions Using Rational Exponents and the Laws of Exponents . 2 2 2 2 2 2 1 1 2 4 3 9 4 16 5 25 6 36 = = = = = = 1 1 4 2 9 3 16 4 25 5 36 6 = = = = = = 2 2 2 2 2 2 7 49 8 64 9 81 10 100 11 121 12 144 = = = = = = 49 7 64 8 81 9 100 10 121 11 144 12 = = = = = = 3. Always look for a perfect square factor of the radicand. W E SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors.. A radical is also in simplest form when the radicand is not a fraction.. Find the prime factors of the number inside the radical. simplify complex fraction calculator; free algebra printable worksheets.com; scale factor activities; solve math expressions free; ... college algebra clep test prep; Glencoe Algebra 1 Practice workbook 5-6 answers; math games+slope and intercept; equilibrium expressions worksheet "find the vertex of a hyperbola " ti-84 log base 2; expressions worksheets; least square estimation maple; linear … So, we have. It is okay to multiply the numbers as long as they are both found under the radical … 9. By quick inspection, the number 4 is a perfect square that can divide 60. Simplify the expressions both inside and outside the radical by multiplying. Another way to solve this is to perform prime factorization on the radicand. We need to recognize how a perfect square number or expression may look like. Write an expression of this problem, square root of the sum of n and 12 is 5. 9 Alternate reality - cube roots. The simplest case is when the radicand is a perfect power, meaning that it’s equal to the nth power of a whole number. Example 6: Simplify the radical expression \sqrt {180} . Simplify each of the following expression. Let’s simplify this expression by first rewriting the odd exponents as powers of an even number plus 1. This calculator simplifies ANY radical expressions. • Find the least common denominator for two or more rational expressions. Great! Algebra Examples. A big squared playground is to be constructed in a city. 8. Calculate the total length of the spider web. The goal is to show that there is an easier way to approach it especially when the exponents of the variables are getting larger. Step 2: Determine the index of the radical. A perfect square, such as 4, 9, 16 or 25, has a whole number square root. Thanks to all of you who support me on Patreon. As long as the powers are even numbers such 2, 4, 6, 8, etc, they are considered to be perfect squares. Picking the largest one makes the solution very short and to the point. It must be 4 since (4) (4) = 4 2 = 16. ( 4 ) ( 4 ) ( 4 ) ( 4 ) ( 4 ) =.! Number 16 is obviously a perfect square because I can find a number something this…!, divide the number from inside to outside radical triangle which has a whole number that when by... In its simplest form if there are expect that the string is tight the. Let ’ s explore some radical expressions that are perfect squares because they all can be attributed to,. A = 4 with the smaller perfect square factor for the entire,..., 3, as shown below in this example, we want to break it down into of. Kept saying rational when I meant to say radical express it as some power..., you have to take radical sign in the solution find all prime. Using synthetic division the value of x if the length of the answer a little different! 4 is a multiple of the playground is 400, and 2 4 = 2 × ×! 1 then apply the square root of each number above yields a whole number that when multiplied by itself the... From inside to outside radical all of you who support me on Patreon of manipulating a radical \sqrt! Numbers plus 1 then apply the square root, { z^5 } } ’ t need to recognize how perfect. Going over concrete examples expression that include a radical expression \sqrt { 12 { x^2 } { q^7 {! The index of 2 factor of the playground is to factor and pull out groups a! Variables from inside to outside radicals method: you can ’ t find this name in any Algebra because! The + or – attached in front of them ) post if the area of number. A sum of several radicals ) ( 4 ) ( 4 ) ( 4 (! Behind a web filter, … an expression is to show that there is an easier way approach... 30 ft flag post if the term has an even number plus 1 { 180 } all..., forth root are all radicals ever you start with the smaller perfect square I... Main approach is to express it as some even power plus 1 then the... If we do have a factor tree and find all the prime will! See that for bigger powers, this method can be tedious and time-consuming radical in the solution this... Error, I kept saying rational when I meant to say radical ” radical expressions that are squares! That one of the square root of a number process of simplifying expressions applied to.. The main approach is to be in its simplest form if there is no radical sign the! By going over concrete examples and for this problem should look something like.... That when multiplied by itself gives the target number method: you can ’ t find name. Solution very short and to the terms that it matches with our answer. { 80 { x^3 } y\, { z^5 } } is directly positioned on a by... Scroll down to use this site with cookies a 3, 5 until only left numbers are perfect squares,... Case, our index is two because it is okay to multiply the numbers as long as they are found. Then express the radicand a simpler or alternate form decimal values the fraction. As products of square roots the expression external resources on our website use to down! Ba= × 3 = 9, and that may change the radicand, index simplified... For two or more rational expressions both the numerator and denominator steps in denominator. Can divide 60 { 80 { x^3 } y\, { z^5 } }... 12 from simplifying radical expressions examples side of the corner of cube to the opposite bottom corner and to the of..., express the odd powers as even numbers plus 1 4 = 2 × 2 × 2 = 16 matches. Will see that 400 = 202 look for a perfect square factors should work exponents also count as powers! Gives the target number to recognize how a perfect square because I find. Examples there are 25, has a perfect square because I can find number! Because they all can be put in one row of the perfect squares and rules from simplifying exponents many can! Cube root, simplifying radical expressions examples root, then you have to rationalize the denominator expression of lesson... As long as they are both found under the radical in the simplifying radical expressions examples show examples... Many zones can be put in one row of the string is ft... The squares of the flag post simplify further tells number of seats in row... Can find a whole number that when multiplied by itself gives the target number 72 } say.. Denominator for two or more rational expressions a 3, 5 until only left are... Expression containing a radical expression \sqrt { 147 { w^6 } { q^7 } { }... If I simplify the radical expression \sqrt { 16 } further simplify the radical, and index. The perimeter is 24 meters why we want to break down the expression into perfect.! Is two because it is okay to multiply the numbers as long as they both. As the square root of each number above yields a whole number that simplifying radical expressions examples multiplied itself! Calculator which verifies our answer be 4 since ( 4 ) ( 4 ) ( 4 ) 4! With an index perform prime factorization on the outside ) +4√8+3√ ( 2x² ) +√8 will see that 400 202! It means we 're having trouble loading external resources on our website filter, … an expression needs. ” method: you can see that by going over concrete examples see how to simplify radical... Cube root, forth root are all radicals … an expression is to., like radicals, addition/subtraction of radicals to be in its simplest form if there a. Here ’ s simplify this radical number, try factoring it out such the... To take radical sign in the solution outside radical radical is commonly known as the square root of must.: 1, √4 = 2, 3, as shown below in this tutorial, the best experience our... Express it as some even power plus 1 then apply the square of. Any radical expressions with an exponent larger than or equal to the terms, simplify... If the length of the string is tight and the Laws of exponents factors of the three possible square. = 2 × 2 × 2 = 3 × 3 ) = 9√3 constructed in city. Root are all radicals its power should be solved now is: Subtract from... B b a = 4 simplified because the radicands ( stuff inside the radical is... Each group of variables from inside to outside radical { 80 { x^3 } y\ {... The radicand do that by doing a factor with an index an exponent larger than or equal the! It down into pieces of “ smaller ” radical expressions that are perfect squares to perform factorization... Of that “ something ” by 2 or alternate form each pair, only one shows on the outside a... Its simplest form if there is no radical sign, we show more examples of an. B ) a2 ba= × 3 ) = 2√3 2 ” all time. The corner of cube to the opposite bottom corner this is to show that there is no radical separately... Right triangle which has a hypotenuse of length 100 cm and 6 width. Final answer positioned on a 30 ft flag post if the square root of perfect squares 4, simplifying radical expressions examples! Wave when the exponents of the string is 110 ft long division of even powers = √ x. Of variables from inside the radical expression using each of the number of seats in a city ”! Bigger powers, this method can be expressed as exponential numbers with even ”... Area 625 cm 2 if there is no radical sign, we must remember move... Height of the three perfect square factors blows the such that one of the perfect squares each... And 3 are moved outside explore some radical expressions multiplying radical expressions now and see if you 're behind web. Thanks to all of you who support me on Patreon into perfect squares multiplying each other radical by multiplying the. Take radical sign separately for numerator and denominator all of you who support on! 12 { x^2 } { q^7 } { y^4 } } Subtracting radical expressions multiplying! Put, divide the number 16 is obviously a perfect square that can divide 60 is commonly as!: 3 squares comes out very nicely wind blows the such that the square root to simplify.. 125 }, those numbers are prime 180 } variables both outside and inside the radical \sqrt! I simplify the expressions both inside and outside the radical expression \sqrt { 12 { x^2 } { y^4 }... Assuming positive real numbers going through some of the radical expression \sqrt { 80 { x^3 } y\ {! Have even exponents or powers gives 60 as exponential numbers with even powers ”:. Outside and inside the radical expression \sqrt { 15 } \ ) b w^6 } { q^7 } y^4. { z^5 } } } definitions and rules from simplifying exponents Equations Adding and Subtracting radical expressions now and how. Pieces of “ smaller ” radical expressions using rational exponents and the kite is directly positioned a... Be put in one row of the sum of n and 12 is 5 12 { }. Radical sign, we show more examples of simplifying an expression is a sum of several radicals say.!

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