advertisement

ALGEBRA O.T.Q. Identify the perfect square in each set. 1. 45, 81, 27, 111 2. 156, 99, 8, 25 3. 256, 84, 12, 1000 4. 35, 216, 196, 72 Find the Prime Factorization of each number. 5. 36 6. 64 7. 196 8. 24 10.2 Simplifying What will I be able to do? Simplify radical expressions using the Product and Quotient Property of Square Roots When simplifying a radical expression, find the factors that are to the nth powers of the radicand and then use the Product Property of Radicals. What is the Product Property of Radicals??? Product Property of Radicals For any positive real numbers a and b, the square root of ab is equal to the square root of a times the square root of b = 1. 8 144x y 5 Factor into squares 144 = 12² = 2 4 2 2 2 12 (x ) (y ) y Product Property of Radicals 2 4 2 2 2 12 (x ) (y ) y 4 12x y 2 y 3 2 2) 7 64n 4 8n 3 Product Property of Radicals 3 2 7 4 64n 8n Factor into cubes if possible 3 3 28 (4) (2) n 3 3 Product Property of Radicals 3 3 3 28 (4) (2) n 3 3 28 4 2 n 224n 3 Now, you try these examples. 2. Quotient For real numbers a and b, Property of b 0 the square root of Radicals is equal to the square root , of a divided by the square root of b = Simplify the expression. 6 x 3 y 1) 3 x x 2 y y x3 y y 6 x 3 y 3 Rationalize the denominator 3 x y y 3 y x y y yy x 3 y 2 y When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. Ex: 5 6 Conjugate: 56 3 2 2 Conjugate: 3 2 2 Simplify: 56 53 Multiply by the conjugate 56 56 53 53 53 53 FOIL numerator and denominator 5 3 5 6 5 18 59 Combine like terms 23 9 5 4 SUMMARY! CLASSWORK Pages 631 – 632 #’s 10 – 34 even, 38 – 44 even, 53(a) HOMEWORK Pages 633 #’s 58, 59, 62, 73, 78