Q. 175 In the following exercises, simp... [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. 175 (page 797)

In the following exercises, simplify.
a. $\sqrt{48} + \sqrt{27}$
b. $\sqrt[3]{54} + \sqrt[3]{128}$
c. $6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320}$

Short Answer

Expert verified

On simplification, we get $- \sqrt{2}, 5 \sqrt[3]{3}, - \sqrt[4]{5}$ respectively

Step by step solution

Part (a) Step 1: Given information

Given the expression $\sqrt{72} - \sqrt{98}$

Part (a) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining we get

$\sqrt{72} - \sqrt{98} = \sqrt{36 路 2} - \sqrt{49 路 2} \sqrt{72} - \sqrt{98} = \sqrt{36} 路 \sqrt{2} - \sqrt{49} 路 \sqrt{2} \sqrt{72} - \sqrt{98} = 6 \sqrt{2} - 7 \sqrt{2} \sqrt{72} - \sqrt{98} = - \sqrt{2}$

Part (b) Step 1: Given information

Given expression $\sqrt[3]{54} + \sqrt[3]{128}$

Part (b) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining we get

$\sqrt[3]{24} + \sqrt[3]{81} = \sqrt[3]{8 路 3} + \sqrt[3]{27 路 3} \sqrt[3]{24} + \sqrt[3]{81} = \sqrt[3]{8} 路 \sqrt[3]{3} + \sqrt[3]{27} 路 \sqrt[3]{3} \sqrt[3]{24} + \sqrt[3]{81} = 2 \sqrt[3]{3} + 3 \sqrt[3]{3} \sqrt[3]{24} + \sqrt[3]{81} = 2 \sqrt[3]{3} + 3 \sqrt[3]{3} \sqrt[3]{24} + \sqrt[3]{81} = 5 \sqrt[3]{3}$

Part (c) Step 1: Given information

Given expression $6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320}$

Part (c) Step 2: Simplifying radical and combining

Simplifying, we get

$\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \frac{1}{2} \sqrt[4]{16 路 5} - \frac{2}{3} \sqrt[4]{81 路 5} \frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \frac{1}{2} \sqrt[4]{16} 路 \sqrt[4]{5} - \frac{2}{3} \sqrt[4]{81} 路 \sqrt[4]{5} \frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \frac{1}{2} 路 2 路 \sqrt[4]{5} - \frac{2}{3} 路 3 路 \sqrt[4]{5} \frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \frac{2}{2} 路 \sqrt[4]{5} - \frac{6}{3} 路 \sqrt[4]{5} \frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \sqrt[4]{5} - 2 \sqrt[4]{5} \frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = - \sqrt[4]{5}$

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91影视

In the following exercises, simplify.
a. $\sqrt{48} + \sqrt{27}$
b. $\sqrt[3]{54} + \sqrt[3]{128}$
c. $6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320}$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and combine like terms

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying the radical and combine like terms

Part (c) Step 1: Given information

Part (c) Step 2: Simplifying radical and combining

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91影视

In the following exercises, simplify.a.48+27b.543+1283c.654-323204

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and combine like terms

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying the radical and combine like terms

Part (c) Step 1: Given information

Part (c) Step 2: Simplifying radical and combining

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
a. $\sqrt{48} + \sqrt{27}$
b. $\sqrt[3]{54} + \sqrt[3]{128}$
c. $6 \sqrt[4]{5} - \frac{3}{2} \sqrt[4]{320}$