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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. 8.101 (page 806)

In the following exercise ,simplify
$(a) \frac{1}{\sqrt[3]{7}} (b) \sqrt[3]{\frac{5}{12}} (c) \frac{5}{\sqrt[3]{9 y}}$

Short Answer

Expert verified

$(a) \frac{\sqrt[3]{49}}{7} (b) \frac{2 \sqrt[3]{90}}{6} (c) \frac{5 \sqrt[3]{81 y^{2}}}{9 y}$

Step by step solution

01

Part (a) Step 1. Given information.

Given expression:

$\frac{1}{\sqrt[3]{7}}$

02

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{7^{2}}$ .

$\frac{1}{\sqrt[3]{7}} = \frac{1}{\sqrt[3]{7}} 脳 \frac{\sqrt[3]{7^{2}}}{\sqrt[3]{7^{2}}} = \frac{\sqrt[3]{7^{2}}}{\sqrt[3]{7^{3}}} = \frac{\sqrt[3]{7^{2}}}{7} = \frac{\sqrt[3]{49}}{7}$

03

Part (b) Step 1. Given information.

Given expression:

$\sqrt[3]{\frac{5}{12}}$

04

Part (b) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{12^{2}}$ .

$\frac{\sqrt[3]{5}}{\sqrt[3]{12}} = \frac{\sqrt[3]{5}}{\sqrt[3]{12}} 脳 \frac{\sqrt[3]{12^{2}}}{\sqrt[3]{12^{2}}} = \frac{\sqrt[3]{5 . 12^{2}}}{12} = \frac{2 \sqrt[3]{90}}{6}$

05

Part (c) Step 1. Given information.

Given expression :

$\frac{5 \sqrt[3]{81 y^{2}}}{9 y}$

06

Part (c) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{9^{2} y^{2}}$ .

$\frac{5}{\sqrt[3]{9 y}} = \frac{5}{\sqrt[3]{9 y}} 脳 \frac{\sqrt[3]{9^{2} y^{2}}}{\sqrt[3]{9^{2} y^{2}}} = \frac{5 \sqrt[3]{9^{2} y^{2}}}{9 y} = \frac{5 \sqrt[3]{81 y^{2}}}{9 y}$

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Most popular questions from this chapter

Simplify:

$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$

Write as a radical expression:

(a) $t^{\frac{1}{2}}$

(b) $m^{\frac{1}{3}}$

(c) $r^{\frac{1}{4}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

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 exercises, solve.

$\sqrt[3]{2 x} = - 2$

See all solutions

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