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Chapter 8: Problem 61

What is a radical equation?

Short Answer

Expert verified
A radical equation is an equation that contains a radical or square root, such as \( \sqrt{x} = 2 \). To solve it, one method is to isolate the radical, then square both sides to eliminate the radical, solve for the variable, and then check the solution to ensure it is not extraneous.

Step by step solution

01

Identify Radical Equation

A radical equation contains the variable under a radical. Example of a radical equation is \( \sqrt{x} = 2 \) where x is the variable under the radical.
02

Solve Radical Equation

In order to get the variable x alone and free from the radical, you can square both sides of the equation. This is done because the square root of a number and the square of a number are inverse operations of each other. \( (\sqrt{x})^2 = 2^2 \) which simplifies to \( x = 4 \)
03

Verify the Solution

Substitute the solution back into the original equation to ensure it's correct. \( \sqrt{4} = 2 \). The verification step is key in radical equations to ensure that obtained solution is not extraneous solution.

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Most popular questions from this chapter

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{16}{\sqrt{11}+3}$$

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$ \frac{1}{4-\sqrt{x}} $$

In Exercises \(53-74\), rationalize each denominator. Simplify, if possible. $$\frac{40}{5-\sqrt{5}}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$25^{-\frac{1}{2}}=-5$$

Simplify by first writing the expression in radical form. If applicable, use a calculator to verify your answer. $$625^{-\frac{3}{4}}$$
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