Q. 174 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. 174 (page 797)

In the following exercises, simplify.
a. $\sqrt{72} - \sqrt{98}$
b. $\sqrt[3]{24} + \sqrt[3]{81}$
c. $\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405}$

Short Answer

Expert verified

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

Simplifying the radical and combining the like term

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

Part (b) Step 1: Given information

Given expression $\sqrt[3]{24} + \sqrt[3]{81}$

Part (b) Step 2: Simplifying and combining the like terms,

Simplifying and combining the like terms, we get

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

Part (c) Step 1: Given information

Given expression $\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405}$

Part (c) Step 2: Simplifying and combining the like terms, we get

Simplifying, we get

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

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91影视

In the following exercises, simplify.
a. $\sqrt{72} - \sqrt{98}$
b. $\sqrt[3]{24} + \sqrt[3]{81}$
c. $\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405}$

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and solving

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying and combining the like terms,

Part (c) Step 1: Given information

Part (c) Step 2: Simplifying and combining the like terms, we get

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91影视

In the following exercises, simplify.a.72-98b.243+813c.12804-234054

Short Answer

Step by step solution

Part (a) Step 1: Given information

Part (a) Step 2: Simplifying the radical and solving

Part (b) Step 1: Given information

Part (b) Step 2: Simplifying and combining the like terms,

Part (c) Step 1: Given information

Part (c) Step 2: Simplifying and combining the like terms, we get

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
a. $\sqrt{72} - \sqrt{98}$
b. $\sqrt[3]{24} + \sqrt[3]{81}$
c. $\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405}$