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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. 12 (page 755)

In the following exercises, simplify.
$(a) \sqrt[3]{27} (b) \sqrt[4]{16} (c) \sqrt[5]{243}$

Short Answer

Expert verified

Hence,

$\begin{array}{l} (a) \sqrt[3]{27} = 3 \\ (b) \sqrt[4]{16} = 2 \\ (c) \sqrt[5]{243} = 3 \end{array}$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenexpressionsare \\ (a) \sqrt[3]{27} (b) \sqrt[4]{16} (c) \sqrt[5]{243} \\ Wehavetosimplifythegivenexpressions. \end{array}$

02

Step 2. Simplify the expression in part (a)

$\begin{array}{l} 鈬� \sqrt[3]{27} = \sqrt[3]{(3)} [鈭� 3^{3} = 27] \\ = 3 \end{array}$

03

Step 3. Simplify the expression in part (b)

$\begin{array}{l} 鈬� \sqrt[4]{16} = \sqrt[4]{{(2)}^{4}} [鈭� 2^{4} = 16] \\ = 2 \end{array}$

04

Step 4. Simplify the expression in part (c)

$\begin{array}{l} 鈬� \sqrt[5]{243} = \sqrt[5]{{(3)}^{5}} [鈭� 3^{5} = 243] \\ = 3 \end{array}$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{5 v - 2} + 5 = 0$

Simplify:

$(a) 2 + \sqrt{98} (b) \frac{6 - \sqrt{45}}{3} .$

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.

(a) $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$

(b) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

(c) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

In the following exercises, simplify.

(a) $- 9^{\frac{3}{2}}$

(b) $- 9^{- \frac{3}{2}}$

(c) ${(- 9)}^{\frac{3}{2}}$

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