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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. 518 (page 853)

In the following exercises, simplify
$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

Short Answer

Expert verified

$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = - \sqrt{11} \sqrt{b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = 4 \sqrt[4]{11 c d}$

Step by step solution

01

Step 1. Given information

We have given,

$(a) \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} (b) 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

02

Step 2. Concept

Here we are going to factor greatest common factor out.

03

Part (a) Step 1. Explanation

We have,

$\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b}$

Factoring our common factor,

$\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = (1 - 5 + 3) \sqrt{11 b}$

$鈬� \sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b} = - \sqrt{11} \sqrt{b}$

04

Part (a) Step 2. Conclusion

Hence, value of $\sqrt{11 b} - 5 \sqrt{11 b} + 3 \sqrt{11 b}$

is $- \sqrt{11} \sqrt{b}$ .

05

Part (b) Step 1. Explanation

We have,

$8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$

Factoring out common factor,

$8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = (8 + 5 - 9) \sqrt[4]{11 c d}$

$鈬� 8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d} = 4 \sqrt[4]{11 c d}$

06

Part (b) Step 2. Conclusion

Hence, value of $8 \sqrt[4]{11 c d} + 5 \sqrt[4]{11 c d} - 9 \sqrt[4]{11 c d}$ is $4 \sqrt[4]{11 c d}$ .

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