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Elementary Algebra Notes Section 8.2 Page 1 of 4 Section 8.2: Multiplying, Dividing, and Simplifying Radicals Big Idea: There are rules for how to multiply and divide expressions with radicals which can lead to simpler radical expressions. Big Skill: You should be able to simplify radicals by switching them between products or quotients of radicals and radicals of products or quotients. Product Rule for Square Roots: For nonnegative real numbers a and b, a b ab (the product of two square roots is the square root of the products) and ab a b (vice-versa; the square root of a product equals the product of the square roots). This second equation is very useful for simplifying radicals, if you can think of the number under the square root as a product of a perfect square and another number. Criteria for a Simplified Radical Expression: There are as few radicals in the expression as possible. The radicands are as small as possible. Practice: Simplify the following radicals as much as possible. 1. 6 11 2. 13 x 3. 10 10 4. 20 5. 60 6. 500 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Elementary Algebra Notes 7. 17 8. 10 50 9. 6 2 Section 8.2 Page 2 of 4 Quotient Rule for Square Roots: For nonnegative real numbers a and b, and b 0, a a (the square root of a quotient is the quotient of the square roots) b b And a a (the quotient of two square roots is the square root of the quotient) b b Practice: Simplify the following radicals as much as possible. 4 10. 49 11. 48 3 12. 5 6 13. 8 50 4 5 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Elementary Algebra Notes Section 8.2 Page 3 of 4 3 7 8 2 14. The Square Root of a Square: For any number a, a 2 a (the square root of a square is the absolute value of squared value) Notice: 4 2 16 4 4 Practice: Simplify the following radicals as much as possible. x4 15. 16. 100 p8 7 y4 17. Product Rule for Radicals: For all real numbers for which the indicated roots exist, n a n b n ab n n a na b b Practice: Simplify the following radicals as much as possible. 18. 3 108 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Elementary Algebra Notes Section 8.2 Page 4 of 4 19. 4 160 20. 4 16 625 21. 3 z9 22. 3 8x6 23. 3 54t 5 24. 3 a15 64 Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.