Chapter 8: Q. 16 (page 755)

In the following exercise, simplify.
(a) $\sqrt[3]{- 64}$
(b) $\sqrt[4]{- 16}$
(c) $\sqrt[5]{- 243}$

Short Answer

Expert verified

Hence,

$\begin{array}{l} (a) \sqrt[3]{- 64} = - 4 \\ (b) \sqrt[4]{- 16} = Norealsolution \\ (c) \sqrt[5]{- 243} = - 3 \end{array}$

Step by step solution

Part a. Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (a) \sqrt[3]{- 64} \\ Wehavetosimplifythegivenexpression. \end{array}$

Step 2. Simplify

$\begin{array}{l} \Rightarrow \sqrt[3]{- 64} = \sqrt[3]{{(- 4)}^{3}} [∵ {(- 4)}^{3} = - 64] \\ = - 4 \end{array}$

Part b. Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (b) \sqrt[4]{- 16} \\ Wehavetosimplifythegivenexpression \end{array}$

Step 2. Simplify

$\begin{array}{l} \Rightarrow \sqrt[4]{- 16} = \sqrt[4]{- 16} \\ [\begin{array}{l} ∵ {(- 2)}^{4} = 16 \\ {(2)}^{4} = 16 \end{array}] \\ Therefore,norealsolutionexists \end{array}$

Part c. Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (c) \sqrt[5]{- 243} \\ Wehavetosimplifythegivenexpression \end{array}$

Step 2. Simplify

$\begin{array}{l} \Rightarrow \sqrt[5]{- 243} = \sqrt[5]{{(- 3)}^{5}} [∵ {(- 3)}^{5} = - 243] \\ = - 3 \end{array}$

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In the following exercise, simplify.
(a) $\sqrt[3]{- 64}$
(b) $\sqrt[4]{- 16}$
(c) $\sqrt[5]{- 243}$

Short Answer

Step by step solution

Part a. Step 1. Given information

Step 2. Simplify

Part b. Step 1. Given information

Step 2. Simplify

Part c. Step 1. Given information

Step 2. Simplify

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In the following exercise, simplify.(a)-643(b)-164(c)-2435

Short Answer

Step by step solution

Part a. Step 1. Given information

Step 2. Simplify

Part b. Step 1. Given information

Step 2. Simplify

Part c. Step 1. Given information

Step 2. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

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Geometry

Study anywhere. Anytime. Across all devices.

In the following exercise, simplify.
(a) $\sqrt[3]{- 64}$
(b) $\sqrt[4]{- 16}$
(c) $\sqrt[5]{- 243}$