3.1 – Evaluate nth Roots and Use Rational Exponents

UNIT 3: ALGEBRA: RATIONAL EXPONENTS AND SQUARE ROOT FUNCTIONS

MM3A2aDefine and understand the properties of nth roots

MM3A2bExtend properties of exponents to include rational exponents

MM3A3dSolve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology

GEORGIA PERFORMANCE STANDARDS

For an integer n greater than 1, if bn = a, then b is an nth root of a.

An nth root of a is written as where n is the index of the radical. If n is odd, then a has one real root. If n is even, then a has two real nth roots if a > 0, one real nth root if a = 0, and no real nth roots if a < 0.

VOCABULARY

How can you write the root of an integer using an exponent?

An nth root of x is written as where n is the index of the radical.

RADICALS AND RATIONAL EXPONENTS

𝑛√𝑥Index

Radicand

RADIAL REVIEW – THINK TREES

RADIAL REVIEW

Solve the Following:

1.

RADIAL REVIEW

Solve the Following:

1. *

2. *

3. 2 * 3

4. *

Solve the Following:.

1.

2. -4

3. -3

RADIAL REVIEW

Rational Exponent Form

a) 95/2 = (91/2)5 = 35 = 243

a)27-2/3 == = =

EVALUATE (A) 95/2 AND (B) 27 -2/3

Radical Form

a) 95/2 = ()5 = 35 = 243

a)27-2/3 == =

EVALUATE (A) 95/2 AND (B) 27 -2/3

Calculator Steps:

USING A CALCULATOR

Solve the equation:

a) -2x6 = -1458

b) (x+2)5 = 35

SOLVE EQUATIONS USING NTH ROOTS

Solve the equation. Round the result to two decimal places:

a) x3 + 17 = 132

b) 2x5 + 73 = 53

c) (x+3)4 = 362

SOLVE EQUATIONS USING NTH ROOTS

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