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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. 8.94 (page 801)

Simplify:
(a) $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$
(b) $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$ is $\frac{5 q^{2}}{6}$

The simplification of $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$ is $\frac{2}{b}$

Step by step solution

01

Part (a) Step 1. Given

An expression $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$

To simplify the expression.

02

Part (a) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}} = \sqrt{\frac{75 q^{5}}{108 q}}$

Remove the common factor

$= \sqrt{\frac{25 q^{4}}{36}}$

03

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}} = \sqrt{\frac{25 q^{4}}{36}}$

$= \frac{5 q^{2}}{6}$

The simplification of the expression is $\frac{5 q^{2}}{6}$

04

Part (b) Step 1. Given

An expression $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$

To simplify the expression.

05

Part (b) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}} = \sqrt[3]{\frac{72 b^{2}}{9 b^{5}}}$

Remove the common factors.

$= \sqrt[3]{\frac{8}{b^{3}}}$

06

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}} = \sqrt[3]{\frac{2^{3}}{b^{3}}}$

$= \frac{2}{b}$

The simplification of the expression is $\frac{2}{b}$

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Most popular questions from this chapter

Simplify:

a. $y^{\frac{3}{4}} 路 y^{\frac{5}{8}}$ b. ${(m^{9})}^{\frac{2}{9}}$ c. $\frac{d^{\frac{1}{5}}}{d^{\frac{6}{5}}}$

Simplify:

(a) $4^{\frac{3}{2}}$

(b) $27^{- \frac{2}{3}}$

(c) $625^{- \frac{3}{4}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{800}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{28 q^{6}}{225}}$

See all solutions

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