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## Algebra (all content)

### Course: Algebra (all content)>Unit 12

Lesson 2: Extraneous solutions of radical equations

# Extraneous solutions of radical equations

Practice some problems before going into the exercise.

## Introduction

### Practice question 1

Caleb is solving the following equation for x.
x, equals, square root of, x, plus, 2, end square root, plus, 7
His first few steps are given below.
\begin{aligned}x-7&=\sqrt{x+2}\\ \\ (x-7)^2&=(\sqrt{x+2})^2\\ \\ x^2-14x+49&=x+2 \end{aligned}
Is it necessary for Caleb to check his answers for extraneous solutions?

### Practice question 2

Elena is solving the following equation for x.
cube root of, 3, x, minus, 5, end cube root, plus, 2, equals, 7
Her first few steps are given below.
\begin{aligned}\sqrt{3x-5}&=5\\ \\ \left(\sqrt{3x-5}\right)^3&=(5)^3\\ \\ 3x-5&=125 \end{aligned}
Is it necessary for Elena to check her answers for extraneous solutions?

### Practice question 3

Addison solves the equation below by first squaring both sides of the equation.
2, x, minus, 1, equals, square root of, 8, minus, x, end square root
What extraneous solution does Addison obtain?
x, equals

### Practice question 4

Which value for the constant d makes x, equals, minus, 1 an extraneous solution in the following equation?
square root of, 8, minus, x, end square root, equals, 2, x, plus, d
d, equals