# Warm-up Find the domain and range from these 3 equations.

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Warm-up Find the domain and range from these 3 equations.

Chapter 6 Section 6-6 Radical Equations

Objectives I can solve equations containing radicals
I can solve equations containing rational exponents I can determine if a solution is Extraneous

Undoing The Square Root
We undo addition with subtraction We undo multiplication with division How do we undo the square root? We square it!!

Radical Equations When solving radical equations make sure only the radical is on the left when you start the problem. (This is like solving absolute value) ALWAYS Check answers. You may get Extraneous Solutions from radicals.

Example 1

Example 2

Example 3

Example 4 .

Undoing Rational Exponents
We undo the square root by Squaring It We undo a rational exponent by using the Reciprocal of that exponent

Undoing Rational Exponents

Solve an equation with a rational exponent
EXAMPLE 4 Solve an equation with a rational exponent Solve (x + 2)3/4 – 1 = 7. (x + 2)3/4 – 1 = 7 Write original equation. (x + 2)3/4 = 8 Add 1 to each side. (x + 2)3/4 4/3 = 84/3 Raise each side to the power . 4 3 x + 2 = (23)4/3 Apply properties of exponents. x + 2 = 24 Simplify. x + 2 = 16 Simplify. x = 14 Subtract 2 from each side.

Homework Worksheet 10-5

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