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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. 13 (page 755)

In the following exercises, simplify.
$(a) \sqrt[3]{512} (b) \sqrt[4]{81} (c) \sqrt[5]{1}$

Short Answer

Expert verified

Hence,

$\begin{array}{l} (a) \sqrt[3]{512} = 8 \\ (b) \sqrt[4]{81} = 3 \\ (c) \sqrt[5]{1} = 1 \end{array}$

Step by step solution

01

Step 1. Given information

$\begin{array}{l} Thegivenexpressionsare \\ (a) \sqrt[3]{512} (b) \sqrt[4]{81} (c) \sqrt[5]{1} \\ Wehavetosimplifythegivenexpressions. \end{array}$

02

Step 2. Simplify the expression in part (a)

$\begin{array}{l} 鈬� \sqrt[3]{512} = \sqrt[3]{{(8)}^{3}} [鈭� 8^{3} = 512] \\ = 8 \end{array}$

03

Step 3. Simplify the expression in part (b)

$\begin{array}{l} 鈬� \sqrt[4]{81} = \sqrt[4]{{(3)}^{4}} [鈭� 3^{4} = 81] \\ = 3 \end{array}$

04

Step 4. Simplify the expression in part (c)

$\begin{array}{l} 鈬� \sqrt[5]{1} = \sqrt[5]{{(1)}^{5}} [鈭� 1^{5} = 1] \\ = 1 \end{array}$

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