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# mac1105_lecture4_1 - L4 nth Roots Rational Exponents nth...

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31 L4 nth Roots; Rational Exponents nth Roots A number b is an nth root of a number a if n ba = . The principal nth root of a real number a is denoted n a (2 ) n and defined as follows: If n is an even number and 0 a , then n a is the nonnegative n th root; 0 a < , then n a is undefined (not a real number) If n is an odd number , then n a is the only real n th root of a number a , and it has the same sign as a . Note : Since n a is an n th root, then ( ) n n aa = . Example : Evaluate the radical expressions. 3 27 5 32

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32 4 81 16 Cancellation Rule for Exponents and Radicals : n n aa = if 2 n and n is even n n = if 3 n and n is odd Important Note : 2 x x = , not x ± . Example : Simplify the expressions. () 4 4 3 4 4 3 6 6 2 5 5 4
33 Rules for Radicals : (we assume that all radicals are defined) () m n m n aa = nn n ab a b = n n n b b = m nm n = kn n km m = Example : Simplify each expression. 3 2 27 10 40 2 3 64 3 4 12 9 16

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34 Simplifying Radicals: 1. Use the cancellation rule for radicals and exponents to remove all possible factors out of the radical.
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mac1105_lecture4_1 - L4 nth Roots Rational Exponents nth...

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