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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. 8.102 (page 806)

In the following exercise ,simplify
$(a) \frac{1}{\sqrt[3]{2}} (b) \sqrt[3]{\frac{3}{20}} (c) \frac{2}{\sqrt[3]{25 n}}$

Short Answer

Expert verified

$(a) \frac{\sqrt[3]{4}}{2} (b) \frac{\sqrt[3]{3} . \sqrt[3]{20^{2}}}{20} (c) \frac{2 \sqrt[3]{25^{2} n^{2}}}{25 n}$

Step by step solution

01

Part (a) Step 1. Given information.

Given expression:

$\frac{1}{\sqrt[3]{2}}$

02

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

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

$\frac{1}{\sqrt[3]{2}} 脳 \frac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}} = \frac{\sqrt[4]{2^{2}}}{2}$

03

Part (b) Step 1. Given information.

Given expression:

$\sqrt[3]{\frac{3}{20}}$

04

Part (b) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{20^{2}}$ .

$\frac{\sqrt[3]{3}}{\sqrt[3]{20}} 脳 \frac{\sqrt[3]{20^{2}}}{\sqrt[3]{20^{2}}} = \frac{\sqrt[3]{3} . \sqrt[3]{20^{2}}}{20}$

05

Part (c) Step 1. Given information.

Given expression :

$\frac{2}{\sqrt[3]{25 n}}$

06

Part (c) Step 2. Finding the solution.

Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt[3]{25^{2} n^{2}}$ .

$\frac{2}{\sqrt[3]{25 n}} 脳 \frac{\sqrt[3]{25^{2} n^{2}}}{\sqrt[3]{25^{2} n^{2}}} = \frac{2 \sqrt[3]{25^{2} n^{2}}}{25 n}$

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Most popular questions from this chapter

In the following exercises, simplify.

(a) $32^{\frac{2}{5}}$

(b) role="math" localid="1644741549807" $27^{- \frac{2}{3}}$

(c) ${(- 25)}^{\frac{1}{2}}$

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

In the following exercises, solve.
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