# 14.4 Equations with Radicals

**Solving by Squaring Both Sides • Isolating a Radical • Solving a Nested Radical Equation**

Equations containing radicals are normally solved by squaring both sides of the equation if the radical represents a square root or by a similar operation for the other roots. However, when we do this, we often introduce *extraneous roots.*

# CAUTION

Thus, it is very important that all solutions be checked in the original equation.

# EXAMPLE 1 Solve by squaring both sides

Solve the equation $\sqrt{x\hspace{0.17em}-\hspace{0.17em}4}\hspace{0.17em}=\hspace{0.17em}2.$

By squaring both sides of the equation, we have

This solution checks when put into the original equation.

# EXAMPLE 2 Solve by squaring both sides

Solve the equation $2\sqrt{3x\hspace{0.17em}-\hspace{0.17em}1}\hspace{0.17em}=\hspace{0.17em}3x\hspace{0.17em}.\hspace{0.17em}$

Squaring both sides of ...

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