Chapter 6

Radical Functions and Rational Exponents

6-5 Solving Square Root and other Radical Equations

What you’ll learn … To solve radical equations

A radical equation is an equation that has a variable in a radicand or has a variable with a rational exponent.

Radical Equation

Not a Radical Equation

Steps for Solving a Radical Equation

1. Get radical by itself.

2. Raise both sides to index power.

3. Solve for x.

4. Check.

Example 1 Solving Radical Equations with Index 2

Solve

2 + √3x-2 = 6

√5x+1 – 6 = 0

Example 2 Solving Radical Equations with Rational Exponents

Solve

2 (x – 2)2/3 = 50

3(x+1)3/5 = 24

Real World Connection

A company manufactures solar cells that produce 0.02 watts of power per square centimeter of surface area. A circular solar cell needs to produce at least 10 watts. What is the minimum radius?

Example 4 Checking for Extraneous Solutions

Solve

√x – 3 + 5 = x

√3x + 2 - √2x + 7 = 0

Example 5 Solving Equations with Two Rational Exponents

Solve

(2x +1)0.5 – (3x+4)0.25 = 0

Solve

(x +1)2/3 – (9x+1)1/3 = 0