SIMPLIFYING SQUARE ROOTS EXAMPLES
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1 SIMPLIFYING SQUARE ROOTS EXAMPLES 1. Definition of a simplified form for a square root The square root of a positive integer is in simplest form if the radicand has no perfect square factor other than one.. Have students analyze the following to see if it is true or false: (ALL ARE TRUE.). 40 = 4 10 = 4 10 = For any numbers a and b, where a 0 and b 0, ab = a b. 10 Product Property of Square Roots 4. Eample: Simplify 7 The Product Property of Square Roots and prime factorization can be used to simplify radical epressions in which the radicand is not a perfect square. 7 Prime factorization Product Property 5. Eample: Simplify 150 The Product Property of Square Roots and prime factorization can be used to simplify radical epressions in which the radicand is not a perfect square Prime factorization Product Property Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
2 . When finding the positive square root of an epression containing variables, you must be sure that the result is not negative. Consider that 5 = 5 and (-5) = 5. When you find 5, however, you want only the principal square root. Therefore, absolute values are used as needed to ensure nonnegative results. = = = 4 = 7. Point out that to simplify a square root with a variable, absolute value symbols are necessary when the variable has an even eponent and the 4 eponent of its square root is odd. For eample in =, since is squared in the answer, it will automatically be positive. In =, in order to guarantee that is positive, is necessary. 8. Eample: Simplify 81y The Product Property of Square Roots and prime factorization can be used to simplify radical epressions in which the radicand is not a perfect square. 81y Product Property 9 y 9 y 9 y Prime factorization 9. Eample: Simplify 4 00a b The Product Property of Square Roots and prime factorization can be used to simplify radical epressions in which the radicand is not a perfect square. Product Property 4 00a b 5 5 a a a a b b b 5 a b b 10a b b Prime factorization Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
3 10. Eample: Simplify Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
4 Name: Date: Class: SIMPLIFYING SQUARE ROOTS WORKSHEET Simplify. Use absolute value symbols when necessary m. y a 4 9a a b Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
5 SIMPLIFYING SQUARE ROOTS WORKSHEET KEY Simplify. Use absolute value symbols when necessary m m Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
6 . y y a a a a a a a a Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
7 a b 5 a b b 4 5 a b b 4 a b 5b Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
8 Student Name: Date: SIMPLIFYING SQUARE ROOTS CHECKLIST 1. On question 1, did the student simplify correctly and use absolute value symbols. On question, did the student simplify correctly and use absolute value symbols. On question, did the student simplify correctly and use absolute value symbols 4. On question 4, did the student simplify correctly and use absolute value symbols 5. On question 5, did the student simplify correctly and use absolute value symbols. On question, did the student simplify correctly and use absolute value symbols Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
9 7. On question 1, did the student simplify correctly and use absolute value symbols 8. On question 8, did the student simplify correctly and use absolute value symbols 9. On question 9, did the student simplify correctly and use absolute value symbols 10. On question 10, did the student simplify correctly and use absolute value symbols 11. On question 11, did the student simplify correctly and use absolute value symbols 1. On question 1, did the student simplify correctly and use absolute value symbols Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
10 1. On question 1, did the student simplify correctly and use absolute value symbols 14. On question 14, did the student simplify correctly and use absolute value symbols 15. On question 15, did the student simplify correctly and use absolute value symbols Total Number of Points Johnny Wolfe Jay High School Santa Rosa County Florida August 11, 001
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