Simplify 2 x y 3x y 3 2 4 5 3 Section P.3 How do we simplify expressions involving radicals and/or rational exponents? If a≥0 and b≥0 and b2 = a, then b is the principal square root of a. b a b a 2 2 a a If a≥0 and b≥0, then ab a b and a b ab • The square root of a product is the product of the square roots. Simplify a) 500 b) 6 x 3 x Solution: a. 500 100 5 b. 6x 3x 6x 3x 100 5 18x 2 9x 2 2 10 5 9x 2 2 9 x 2 2 3x 2 Simplify a) 75 b) 5 x 15 x If a≥0 and b>0, then a a b b and a b a . b • The square root of the quotient is the quotient of the square roots. Simplify: 100 9 Solution: 100 100 10 9 9 3 Simplify: a) 49 16 b) 36 144 Read Section P.3 Page 32 #1-25 odd Graphing calculator check-out ◦ Textbook window ◦ Need signed form ◦ Must have your ID or schedule Evaluate each expression in Exercises 1-6 or indicate that the root is not a real number. 1) 36 3) 36 13 2 5) Use the product rule to simplify the expressions in Exercises 7-16. In Exercises 11-16, assume the variables represent nonnegative real numbers. 7) 50 9) 11) 45 x 2 2x 6x 3 13) x 15) 2x2 6x Simplify 4 3 32 3 3 3 Simplify 2 5 5 5 5 4 5 Simplify 24 2 6 4 6 Simplify 18 5 8 13 2 a) 12 x 15 x 25 36 b) 3 54 2 24 96 4 63 2 28 We DO NOT leave radicals in the denominator Multiply numerator and denominator by the smallest number that will eliminate the radical. If square root: can multiply top and bottom by the radical in the denominator, then simplify a) 6 18 b) 7 3 a) 5 3 b) 6 12 For a denominator of form a b , we multiply numerator and denominator by its conjugate, a b 5 3 7 4 6 5 n a b n means that b a If n, the index, is even, then a > 0 and b > 0. If n is odd, a and b can be any real numbers. For all real numbers, where the indicated roots represent real numbers, n a b ab and n n n n a n a , b0 b b 3 a) 54 b) 8 8 4 4 8 c) 3 125 3 a) 40 b) 8 8 5 5 27 c) 3 1000 3 32 2 2 4 4 3 81 4 3 3 3 Read Section P.3 Page 32 #27-75 odd You have until 1:50 to work on this assignment. We will then finish the P.3 notes. a 1 /n n a. Furthermore, 1 1 1/ n a 1/ n n , a 0 a a a) 4 1 2 b) 16 1 4 c) 27 1 3 1 4 a) 81 1 3 b) 125 c) 64 1 3 a m/ n m n m ( a) a . n The exponent m/n consists of two parts: the denominator n is the index of the radical and the numerator m is the exponent. Furthermore, a m/n 1 a m/n . a) 9 3 2 b) 125 2 3 c) 16 3 4 a) 4 3 2 b) 32 2 5 c) 8 5 3 a) 3x 34 2 x 12 43 12 x b) 1 4 6x a) 2 x 43 5x 83 4 20 x b) 3 2 5x Page 32 #77-93 odd, 104, 106, 121 In Exercises 77-84, evaluate each expression without using a calculator. 77) 361 2 79) 81 3 83) 324 5 81) 1252 3 In Exercises 85-94, simplify using properties of exponents. 3 85) 7 x 2 x 13 12 87) 20 x 14 5x 14 89) 91) x 25 x y 3 y 23 4 6 12 14 3 93) y 1 12