Q. 740 - Review Exercises In the following exercises, simp... [FREE SOLUTION]

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Math
Elementary Algebra
Chapter 9
Q. 740 - Review Exercises

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 740 - Review Exercises (page 1152)

In the following exercises, simplify.
$\sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}}$

Short Answer

Expert verified

The expression $\sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}}$ simplifies to $\begin{array}{rcl} 4 c 路 \sqrt[3]{10 c^{2}} + 2 c 路 \sqrt[3]{10} \end{array}$ .

Step by step solution

Step 1. Given Information

We are given an expression $\sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}}$ .

We need to simplify the expression.

Step 2. Simplify the expression

Rewrite each radicand using perfect cube factors.

$\begin{array}{rcl} \sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}} & = & \sqrt[3]{64 c^{3} 路 10 c^{2}} - \sqrt[3]{(- 8 c^{3}) 路 10} \\ = & \sqrt[3]{64 c^{3}} 路 \sqrt[3]{10 c^{2}} - \sqrt[3]{(- 8 c^{3})} 路 \sqrt[3]{10} \end{array}$

Rewrite the perfect cubes.

$\begin{array}{rcl} \sqrt[3]{64 c^{3}} 路 \sqrt[3]{10 c^{2}} - \sqrt[3]{(- 8 c^{3})} 路 \sqrt[3]{10} & = & \sqrt[3]{{(4 c)}^{3}} 路 \sqrt[3]{10 c^{2}} - \sqrt[3]{{(- 2 c)}^{3}} 路 \sqrt[3]{10} \end{array}$

Simplify the radicals where possible.

$\begin{array}{rcl} \sqrt[3]{{(4 c)}^{3}} 路 \sqrt[3]{10 c^{2}} - \sqrt[3]{{(- 2 c)}^{3}} 路 \sqrt[3]{10} & = & 4 c 路 \sqrt[3]{10 c^{2}} - (- 2 c) 路 \sqrt[3]{10} \\ = & 4 c 路 \sqrt[3]{10 c^{2}} + 2 c 路 \sqrt[3]{10} \end{array}$

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91影视

In the following exercises, simplify.
$\sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplify the expression

One App. One Place for Learning.

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91影视

In the following exercises, simplify.640c53--80c33

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Geometry

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\sqrt[3]{640 c^{5}} - \sqrt[3]{- 80 c^{3}}$