Q. 8.76 Simplify27+43453-7403聽121283-53... [FREE SOLUTION]

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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. 8.76 (page 791)

Simplify
$\sqrt{27} + 4 \sqrt{3}$
$4 \sqrt[3]{5} - 7 \sqrt[3]{40}$
$\frac{1}{2} \sqrt[3]{128} - \frac{5}{3} \sqrt[3]{54}$

Short Answer

Expert verified

Part a. $7 \sqrt{3}$

Part b. $- 10 \sqrt[3]{5}$

Part c. $- 3 \sqrt[3]{2}$

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} 路 \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \sqrt{27} + 4 \sqrt{3} & = & \sqrt{9 路 3} + 4 \sqrt{3} \\ = & \sqrt{9} 路 \sqrt{3} + 4 \sqrt{3} \\ = & 3 \sqrt{3} + 4 \sqrt{3} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 3 \sqrt{3} + 4 \sqrt{3} & = & (3 + 4) \sqrt{3} \\ = & 7 \sqrt{3} \end{array}$

Part (b) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} 路 \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} 4 \sqrt[3]{5} - 7 \sqrt[3]{40} & = & 4 \sqrt[3]{5} - 7 \sqrt[3]{8 路 5} \\ = & 4 \sqrt[3]{5} - 7 \sqrt[3]{8} 路 \sqrt[3]{5} \\ = & 4 \sqrt[3]{5} - 7 路 2 路 \sqrt[3]{5} \\ = & 4 \sqrt[3]{5} - 14 \sqrt[3]{5} \end{array}$

On combing the like radicals we get

$\begin{array}{rcl} 4 \sqrt[3]{5} - 14 \sqrt[3]{5} & = & (4 - 14) \sqrt[3]{5} \\ = & - 10 \sqrt[3]{5} \end{array}$

Part (c) Step 1. Simplify the radicals and combine like radicals

Using $\sqrt{a b} = \sqrt{a} 路 \sqrt{b}$ simplify the expression.

$\begin{array}{rcl} \frac{1}{2} \sqrt[3]{128} - \frac{5}{3} \sqrt[3]{54} & = & \frac{1}{2} \sqrt[3]{128} - \frac{5}{3} \sqrt[3]{54} \\ = & \frac{1}{2} \sqrt[3]{64 路 2} - \frac{5}{3} \sqrt[3]{27 路 2} \\ = & \frac{1}{2} \sqrt[3]{64} 路 \sqrt[3]{2} - \frac{5}{3} \sqrt[3]{27} 路 \sqrt[3]{2} \\ = & \frac{1}{2} 路 4 路 \sqrt[3]{2} - \frac{5}{3} 路 3 路 \sqrt[3]{2} \\ = & 2 \sqrt[3]{2} - 5 \sqrt[3]{2} \end{array}$

On combing the like radicals we get

role="math" localid="1644812399604" $\begin{array}{rcl} 2 \sqrt[3]{2} - 5 \sqrt[3]{2} & = & (2 - 5) \sqrt[3]{2} \\ = & - 3 \sqrt[3]{2} \end{array}$

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91影视

Simplify
$\sqrt{27} + 4 \sqrt{3}$
$4 \sqrt[3]{5} - 7 \sqrt[3]{40}$
$\frac{1}{2} \sqrt[3]{128} - \frac{5}{3} \sqrt[3]{54}$

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

Part (c) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

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91影视

Simplify27+43453-7403121283-53543

Short Answer

Step by step solution

Part (a) Step 1. Simplify the radicals and combine like radicals

Part (b) Step 1. Simplify the radicals and combine like radicals

Part (c) Step 1. Simplify the radicals and combine like radicals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Simplify
$\sqrt{27} + 4 \sqrt{3}$
$4 \sqrt[3]{5} - 7 \sqrt[3]{40}$
$\frac{1}{2} \sqrt[3]{128} - \frac{5}{3} \sqrt[3]{54}$