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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. 8.103 (page 807)

In the following exercise ,simplify
$(a) \frac{1}{\sqrt[4]{3}} (b) \sqrt[4]{\frac{3}{64}} (c) \frac{3}{\sqrt[4]{125 x}}$

Short Answer

Expert verified

$(a) \frac{\sqrt[4]{27}}{3} (b) \frac{\sqrt[4]{12}}{4} (c) \frac{3 \sqrt[4]{5 x^{3}}}{5 x}$

Step by step solution

01

Part (a) Step 1. Given information.

Given expression:

$\frac{1}{\sqrt[4]{3}}$

02

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[4]{3^{3}}$ .

$\frac{1}{\sqrt[4]{3}} 脳 \frac{\sqrt[4]{3^{3}}}{\sqrt[4]{3^{3}}} = \frac{\sqrt[4]{27}}{3}$

03

Part (b) Step 1. Given information.

Given expression:

$\sqrt[4]{\frac{3}{64}}$

04

Part (b) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[4]{4^{3}}$ . $\frac{\sqrt[4]{3}}{\sqrt[4]{64}} = \frac{\sqrt[4]{3}}{\sqrt[4]{2^{4} . 2^{2}}} = \frac{\sqrt[4]{3}}{2 . \sqrt[4]{4}} 脳 \frac{\sqrt[4]{4^{3}}}{\sqrt[4]{4^{3}}} = \frac{\sqrt[4]{3}}{2.4} . \sqrt[4]{4^{3}} = \frac{\sqrt[4]{3}}{8} . \sqrt[4]{2^{4} . 2^{2}} = \frac{\sqrt[4]{3}}{4} . \sqrt[4]{4}$

05

Part (c) Step 1. Given information.

Given expression :

$\frac{3}{\sqrt[4]{125 x}}$

06

Part (c) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\frac{\sqrt[4]{5 x^{3}}}{\sqrt[4]{5 x^{3}}}$ .

$\frac{3}{\sqrt[4]{125 x}} = \frac{3}{\sqrt[4]{5^{3} x}} = \frac{3}{\sqrt[4]{5^{3} x}} 脳 \frac{\sqrt[4]{5 x^{3}}}{\sqrt[4]{5 x^{3}}} = \frac{3 \sqrt[4]{5 x^{3}}}{5 x}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}$

(b) $\sqrt[3]{\frac{5 x^{6} y^{9}}{40 x^{5} y^{3}}}$

(c) $\sqrt[4]{\frac{5 a^{8} b^{6}}{80 a^{3} b^{2}}}$

In the following exercise, write as a radical expression.

鈸� x^{\frac{1}{2}} 鈸� y^{\frac{1}{3}} 鈸� z^{\frac{1}{4}}

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98 r^{5}}{100}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{675}$

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