Chapter 8: Q.530 (page 854)

In the following exercises, simplify
$a) \frac{\sqrt{48}}{\sqrt{75}} b) \frac{\sqrt[3]{81}}{\sqrt[3]{24}}$

Short Answer

Expert verified

Simplifying,

$a) \frac{\sqrt{48}}{\sqrt{75}} = \frac{4}{5} b) \frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \frac{3}{2}$

Step by step solution

Step 1. Given information

We have given,

$\frac{\sqrt{48}}{\sqrt{75}}$

Step 2. Concept

Here we will use the quotient rule of the radical.

Quotient rule of the radical: $\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$

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

Part (a) Step 1. Explanation

We have,

$\frac{\sqrt{48}}{\sqrt{75}}$

Applying quotient rule of the radical,

$\frac{\sqrt{48}}{\sqrt{75}} = \sqrt{\frac{48}{75}}$

Canceling greatest common factor,

$\frac{\sqrt{48}}{\sqrt{75}} = \sqrt{\frac{16 \cdot 3}{25 \cdot 3}}$

$\Rightarrow \frac{\sqrt{48}}{\sqrt{75}} = \sqrt{\frac{16}{25}}$

$\Rightarrow \frac{\sqrt{48}}{\sqrt{75}} = \frac{4}{5}$

Part (a) Step 2. Conclusion

Hence, simplifying $\frac{\sqrt{48}}{\sqrt{75}}$ we will get, $\frac{4}{5}$ .

Part (b) Step 2. Explanation

We have,

$\frac{\sqrt[3]{81}}{\sqrt[3]{24}}$

Using quotient rule of the radical,

$\frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \sqrt[3]{\frac{81}{24}}$

Factoring greatest common factor out,

$\frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \sqrt[3]{\frac{27 \cdot 3}{8 \cdot 3}}$

Rewriting it,

$\frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \sqrt[3]{\frac{3^{3}}{2^{3}}}$

role="math" localid="1645704504957" $\Rightarrow \frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \sqrt[3]{{(\frac{3}{2})}^{3}}$

Applying radical rule,

role="math" localid="1645704553841" $\frac{\sqrt[3]{81}}{\sqrt[3]{24}} = \frac{3}{2}$

Part (b) Step 2. Conclusion

Hence, simplifying $\frac{\sqrt[3]{81}}{\sqrt[3]{24}}$ we will get $\frac{3}{2}$ .

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In the following exercises, simplify
$a) \frac{\sqrt{48}}{\sqrt{75}} b) \frac{\sqrt[3]{81}}{\sqrt[3]{24}}$

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 2. Explanation

Part (b) Step 2. Conclusion

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In the following exercises, simplifya)4875b)813243

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 2. Explanation

Part (b) Step 2. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, simplify
$a) \frac{\sqrt{48}}{\sqrt{75}} b) \frac{\sqrt[3]{81}}{\sqrt[3]{24}}$