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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 9.135. (page 1085)

Simplify: $\sqrt{\frac{7}{18}}$ .

Short Answer

Expert verified

Simplified form of $\sqrt{\frac{7}{18}}$ is $\frac{\sqrt{14}}{6}$ .

Step by step solution

01

Step 1. Given information.

Given a fraction $\sqrt{\frac{7}{18}}$ .

02

Step 2. Check if the fraction is a perfect square.

The fraction is not a perfect square.

So, rewrite using the quotient property.

Quotient property of square roots says that if a, b are non-negative number and $b 鈮� 0$ , then $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ .

It follows that $\sqrt{\frac{7}{18}} = \frac{\sqrt{7}}{\sqrt{18}}$ .

03

Step 3. Simplify the denominator.

Simplify the denominator as $\frac{\sqrt{7}}{\sqrt{18}} = \frac{\sqrt{7}}{3 \sqrt{2}}$ .

04

Step 4. Rationalize the denominator and simplify.

Rationalize the denominator by multiplying both numerator and denominator by $\sqrt{2}$ .

Rationalize and simplify as follows.

$\begin{array}{rcl} \frac{\sqrt{7}}{3 \sqrt{2}} & = & \frac{\sqrt{7} 路 \sqrt{2}}{3 \sqrt{2} 路 \sqrt{2}} \\ = & \frac{\sqrt{14}}{3 路 2} \\ = & \frac{\sqrt{14}}{6} \end{array}$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{2 y + 4} + 6 = 0$

For the equation $\sqrt{- x + 2} = x$ :

Part (a): Is $x = - 2$ a solution?

Part (b): Is $x = 1$ a solution?

In the following exercises, simplify and rationalize the denominator.

$\sqrt{\frac{7}{40}}$

In the following exercises, simplify by rationalizing the denominator

(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

In the following exercises, simplify by rationalizing the denominator

(a) $\frac{3}{3 + \sqrt{11}}$ (b) $\frac{8}{1 - \sqrt{5}}$

See all solutions

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