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

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 $\sqrt{10}$ ,

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

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" $\frac{8}{\sqrt{2 y}} = \frac{8 \cdot \sqrt{2 y}}{\sqrt{2 y} \cdot \sqrt{2 y}}$

Simplifying,

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

$\Rightarrow \frac{8}{\sqrt{2 y}} = \frac{4 \sqrt{2 y}}{y}$

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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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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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

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In the following exercises, rationalize the denominator.
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