Chapter 8: Q.524 (page 853)

In the following exercises, multiply
$a) \sqrt{11} (8 + 4 \sqrt{11}) b) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$

Short Answer

Expert verified

Simplifying,

$a) \sqrt{11} (8 + 4 \sqrt{11}) = 8 \sqrt{11} + 44 b) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18}) = 3 + 3 \sqrt[3]{2}$

Step by step solution

Step 1. Given information

We have given,

$a) \sqrt{11} (8 + 4 \sqrt{11}) b) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$

Step 2. Concept

Here we will use the distributive property,

$a (b + c) = a b + a c$

and multiplication rule of radical,

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

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

Part (a) Step 1. Explanation

We have given,

$\sqrt{11} (8 + 4 \sqrt{11})$

Using distributive property,

$\sqrt{11} \cdot 8 + \sqrt{11} \cdot 4 \sqrt{11}$

Using product rule of the radical,

role="math" localid="1645688897594" $\sqrt{11} \cdot 8 + \sqrt{11^{2}} \cdot 4$

$\Rightarrow \sqrt{11} \cdot 8 + 44$

Part (a) Step 2. Conclusion

Hence, multiplying and simplifying $\sqrt{11} (8 + 4 \sqrt{11})$ we will get, $\sqrt{11} \cdot 8 + 44$ .

Part (b) Step 1. Explanation

We have,

$\sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$

Using distributive property,

$\sqrt[3]{3} \cdot \sqrt[3]{9} + \sqrt[3]{3} \cdot \sqrt[3]{18}$

role="math" localid="1645689203181" $\Rightarrow \sqrt[3]{3} \cdot \sqrt[3]{3 \cdot 3} + \sqrt[3]{3} \cdot \sqrt[3]{3 \cdot 3 \cdot 2}$

$\Rightarrow \sqrt[3]{3^{3}} + \sqrt[3]{3^{3}} \cdot \sqrt[3]{2}$

$\Rightarrow 3 + 3 \cdot \sqrt[3]{2}$

Part (b) Step 1. Explanation

Hence, multiplying and simplifying $\sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$ we will get $3 + 3 \sqrt[3]{2}$

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In the following exercises, multiply
$a) \sqrt{11} (8 + 4 \sqrt{11}) b) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$

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 1. Explanation

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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 1. Explanation

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Most popular questions from this chapter

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In the following exercises, multiply
$a) \sqrt{11} (8 + 4 \sqrt{11}) b) \sqrt[3]{3} (\sqrt[3]{9} + \sqrt[3]{18})$