Algebra IIAlgebra II6.1: Evaluate nth Roots and 6.1: Evaluate nth Roots and

Use Rational ExponentsUse Rational Exponents

Simplify the expression.Simplify the expression.

Simplify the expression.Simplify the expression.

Simplify the expression.Simplify the expression.

Simplify the expression.Simplify the expression.

Finding real Finding real nnth roots of th roots of a.a.

If If bbnn = = aa, then , then bb is an is an nnth root th root of of aa..

Don’t forget about for even Don’t forget about for even roots.roots.2222 = 4 and (-2) = 4 and (-2)22 = 4, therefore = 4, therefore

the 2the 2ndnd root of 4 would be 2. root of 4 would be 2.

Examples: Find the indicated Examples: Find the indicated realreal nnth root(s) of th root(s) of a a without without

using a calculator.using a calculator.1.) 1.) nn = 3, = 3, aa = -64 = -64

2.) 2.) nn = 3, = 3, aa = 216 = 216

Examples: Find the indicated Examples: Find the indicated realreal nnth root(s) of th root(s) of a a without without

using a calculator.using a calculator.3.) 3.) nn = 4, = 4, aa = -16 = -16

4.) n = 4, a = 814.) n = 4, a = 81

Examples: Find the indicated Examples: Find the indicated realreal nnth root(s) of th root(s) of a a without without

using a calculator.using a calculator.5.) 5.) nn = 5, = 5, aa = 0 = 0

6.) n = 5, a = 2436.) n = 5, a = 243

Rational Exponents – Key Rational Exponents – Key ConceptConcept

Rewrite the expression Rewrite the expression using rational exponent using rational exponent

notation.notation.

Rewrite the expression Rewrite the expression using radical notation.using radical notation.

Evaluate the expression Evaluate the expression without using a calculator.without using a calculator.

Evaluate the expression Evaluate the expression without using a calculator.without using a calculator.

Evaluate the expression using a Evaluate the expression using a calculator. Round to the nearest calculator. Round to the nearest

hundredth.hundredth.