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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.100 (page 804)

In the following exercise ,simplify
$(a) \frac{6}{\sqrt{5}} (b) \sqrt{\frac{7}{18}} (c) \frac{5}{\sqrt{5 x}}$

Short Answer

Expert verified

$(a) \frac{6 \sqrt{5}}{5} (b) \frac{\sqrt{14}}{6} (c) \frac{\sqrt{5 x}}{x}$

Step by step solution

01

Part (a) Step 1. Given information.

The expression given :

$\frac{6}{\sqrt{5}}$

02

Part (a) Step 2. Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{5}$ .

$\frac{6}{\sqrt{5}} = \frac{6}{\sqrt{5}} 脳 \frac{\sqrt{5}}{\sqrt{5}} = \frac{6 \sqrt{5}}{5}$

03

Part (b) Step 1. Given information.

Given expression:

$\sqrt{\frac{7}{18}}$

04

Part (b) Step 2. Finding solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{18}$ .

$\sqrt{\frac{7}{18}} = \frac{\sqrt{7}}{\sqrt{18}} 脳 \frac{\sqrt{18}}{\sqrt{18}} = \frac{\sqrt{7} \sqrt{18}}{18} = \frac{\sqrt{7} . 9}{18} = \frac{\sqrt{7}}{2}$

05

Part (c) Step 1. Given information

Given expression:

$\frac{5}{\sqrt{5 x}}$

06

Part (c) Step 2. Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{5 x}$ .

$\frac{5}{\sqrt{5 x}} = \frac{5}{\sqrt{5 x}} 脳 \frac{\sqrt{5 x}}{\sqrt{5 x}} = \frac{5 \sqrt{5 x}}{5 x} = \frac{\sqrt{5 x}}{x}$

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