Q.532 In the following exercises, rati... [FREE SOLUTION]

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Intermediate Algebra

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$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q.532 (page 854)

In the following exercises, rationalize the denominator.
$a) \frac{8}{\sqrt{3}} b) \sqrt{\frac{7}{40}} c) \frac{8}{\sqrt{2 y}}$

Short Answer

Expert verified

Simplifying,

$a) \frac{8}{\sqrt{3}} = \frac{8 \sqrt{3}}{3} b) \sqrt{\frac{7}{40}} = \frac{\sqrt{70}}{40} c) \frac{8}{\sqrt{2 y}} = \frac{4 \sqrt{2 y}}{y}$

Step by step solution

Step 1. Given information

We have given,

$a) \frac{8}{\sqrt{3}} b) \sqrt{\frac{7}{40}} c) \frac{8}{\sqrt{2 y}}$

Step 2. Concept

To rationalize the denominator we will multiply numerator and denominator by conjugate of denominator.

Also we will use radical rule,

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$\sqrt[n]{a} \sqrt[n]{b} = \sqrt[n]{a b}$

$\sqrt[n]{a^{n}} = a$

Part (a) Step 1. Explanation

We have,

$\frac{8}{\sqrt{3}}$

Multiplying numerator and denominator by $\sqrt{3}$ ,

$\frac{8}{\sqrt{3}} = \frac{8 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

localid="1645707223215" $鈬� \frac{8}{\sqrt{3}} = \frac{8 \sqrt{3}}{3}$

Part (a) Step 2. Conclusion

Hence, rationalizing $\frac{8}{\sqrt{3}}$ we will get $\frac{8 \sqrt{3}}{3}$ .

Part (b) Step 1. Explanation

We have,

$\sqrt{\frac{7}{40}}$

Rewriting it,

$\sqrt{\frac{7}{40}} = \frac{\sqrt{7}}{\sqrt{40}}$

Simplifying,

$\sqrt{\frac{7}{40}} = \frac{\sqrt{7}}{4 \sqrt{10}}$

Multiplying numerator and denominator by $\sqrt{10}$ ,

$\sqrt{\frac{7}{40}} = \frac{\sqrt{7} 路 \sqrt{10}}{4 \sqrt{10} 路 \sqrt{10}}$

Using radical rule,

$\sqrt{\frac{7}{40}} = \frac{\sqrt{70}}{40}$

Part (b) Step 2. Conclusion

Hence, rationalizing $\sqrt{\frac{7}{40}}$ we will get $\frac{\sqrt{70}}{40}$ .

Part (c) Step 1. Explanation

We have,

$\frac{8}{\sqrt{2 y}}$

Multiplying numerator and denominator by $\sqrt{2 y}$ ,

localid="1645707787385" $\frac{8}{\sqrt{2 y}} = \frac{8 路 \sqrt{2 y}}{\sqrt{2 y} 路 \sqrt{2 y}}$

Simplifying,

$\frac{8}{\sqrt{2 y}} = \frac{8 路 \sqrt{2 y}}{2 y}$

$鈬� \frac{8}{\sqrt{2 y}} = \frac{4 \sqrt{2 y}}{y}$

Part (c) Step 2. Conclusion

Hence, rationalizing $\frac{8}{\sqrt{2 y}}$ we will get, $\frac{4 \sqrt{2 y}}{y}$ .

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91影视

In the following exercises, rationalize the denominator.
$a) \frac{8}{\sqrt{3}} b) \sqrt{\frac{7}{40}} c) \frac{8}{\sqrt{2 y}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept

Part (a) Step 1. Explanation

Part (a) Step 2. Conclusion

Part (b) Step 1. Explanation

Part (b) Step 2. Conclusion

Part (c) Step 1. Explanation

Part (c) Step 2. Conclusion

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91影视

In the following exercises, rationalize the denominator.a)83b)740c)82y

Short Answer

Step by step solution

Step 1. Given information

Step 2. Concept

Part (a) Step 1. Explanation

Part (a) Step 2. Conclusion

Part (b) Step 1. Explanation

Part (b) Step 2. Conclusion

Part (c) Step 1. Explanation

Part (c) Step 2. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In the following exercises, rationalize the denominator.
$a) \frac{8}{\sqrt{3}} b) \sqrt{\frac{7}{40}} c) \frac{8}{\sqrt{2 y}}$