Chapter 8: Q.523 (page 853)

In the following exercises, simplify.
$a) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) b) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Short Answer

Expert verified

Simplifying,

$a) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) = 126 x^{2} \sqrt{x} b) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}}) = 48 a \sqrt[3]{5 a^{2}}$

Step by step solution

Step 1. Given information

We have given,

$a) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) b) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Step 2. Concept

Here we can use the product property of nth root.

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

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

Part (a) Step 1. Explanation

We have,

$(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$

Rewriting it,

role="math" localid="1645687331380" $21 x^{2} \sqrt{18 \cdot 2 x}$

role="math" localid="1645687250527" $\Rightarrow 21 x^{2} \sqrt{36 x}$

$\Rightarrow 126 x^{2} \sqrt{x}$

Part (a) Step 2. Conclusion

Hence, value of $(3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}})$ is $126 x^{2} \sqrt{x}$ .

Part (b) Step 1. Explanation

We have given,

$(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

Rewriting it we will get,

$12 \sqrt[3]{4 \cdot 5 a^{2} \cdot 4 \cdot 4 a^{3}}$

$\Rightarrow 48 a \sqrt[3]{5 a^{2}}$

Part (b) Step 2. Conclusion

Hence, value of $(- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$ is $48 a \sqrt[3]{5 a^{2}}$ .

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In the following exercises, simplify.
$a) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) b) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$

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

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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

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Most popular questions from this chapter

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In the following exercises, simplify.
$a) (3 \sqrt{2 x^{3}}) (7 \sqrt{18 x^{2}}) b) (- 6 \sqrt[3]{20 a^{2}}) (- 2 \sqrt[3]{16 a^{3}})$