Algebra II 6.1: Evaluate nth Roots and Use Rational Exponents

Simplify the expression.

Finding real nth roots of a. If b n = a, then b is an nth root of a. If b n = a, then b is an nth root of a. Don’t forget about for even roots. Don’t forget about for even roots. 2 2 = 4 and (-2) 2 = 4, therefore the 2 nd root of 4 would be = 4 and (-2) 2 = 4, therefore the 2 nd root of 4 would be 2.

Examples: Find the indicated real nth root(s) of a without using a calculator. 1.) n = 3, a = ) n = 3, a = 216

Examples: Find the indicated real nth root(s) of a without using a calculator. 3.) n = 4, a = ) n = 4, a = 81

Examples: Find the indicated real nth root(s) of a without using a calculator. 5.) n = 5, a = 0 6.) n = 5, a = 243

Rational Exponents – Key Concept

Rewrite the expression using rational exponent notation.

Rewrite the expression using radical notation.

Evaluate the expression without using a calculator.

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