7.1 Roots and Rational Exponents

Objective: to rewrite radicals in rational exponent notation and evaluate radicals

Vocabulary

• nth root is defined as

• n is called the index of the radical

n nb a a b

Real nth roots

Examples

3 4

1. 3, 27 2. 4, 16

27 16

n a n a

Find the indicated real nth root(s) of a

• If is an nth root of a and m is some positive integer:1

na

1

( ) ( )m

nm m mnn na a a a

Examples: Change from exponent form to radical form

2 4

3 5

55

102

y

x

z x

Examples: Change from radical form to exponent form.

23

58 74

( )

( )

x x

x z

Examples: Evaluating Expressions with Rational Exponents

23

529 32

You Try!

23( 8) ? 3 64 ?

24 16 ? 3 125 ?

Approximating Root with a calculator

Examples: Solving Equations Using nth roots

4 31. 2 162 2. ( 3) =27x x

Assignment

Read Section 7.1

Pgs. 404-406: 13-22 all, 29, 30, 32, 34, 35, 37, 38, 40, 53, 55, 56, 59, 60, 78-84 even