Chapter 8: Q.522 (page 853)

In the following exercises, simplify.
$(a) (5 \sqrt{6}) (- \sqrt{12}) (b) (- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$

Short Answer

Expert verified

Simplifying,

$(a) (5 \sqrt{6}) (- \sqrt{12}) = - 30 \sqrt{2} (b) (- 2 \sqrt[4]{18}) (- \sqrt[4]{9}) = 6 \sqrt[4]{2}$

Step by step solution

Step 1. Given information

We have given,

$(a) (5 \sqrt{6}) (- \sqrt{12}) (b) (- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$

Step 2. Concept

Here we can use the product property of nth root.

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

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

Part (a) Step 1. Explanation

Here we have given,

$(5 \sqrt{6}) (- \sqrt{12})$

Using product property of nth root,

$(5 \sqrt{6}) (- \sqrt{12}) = - 5 \sqrt{6 \times 12}$

Simplifying,

role="math" localid="1645119124722" $(5 \sqrt{6}) (- \sqrt{12}) = - 5 \sqrt{36 \times 2} = - 5 \sqrt{6^{2} \times 2} = - 5 \sqrt{6^{2}} \cdot \sqrt{2} = - 30 \sqrt{2}$

Part (a) Step 2. Conclusion

Hence, value of $(5 \sqrt{6}) (- \sqrt{12})$ is $- 30 \sqrt{2}$ .

Part (b) Step 1. Explanation

We have,

$(- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$

Multiplication of two negative numbers is positive.

$2 \sqrt[4]{18} \cdot \sqrt[4]{9}$

Rewriting it,

$2 \sqrt[4]{18 \cdot 9}$

$\Rightarrow 2 \sqrt[4]{9 \cdot 2 \cdot 9}$

$\Rightarrow 2 \sqrt[4]{3^{4} \cdot 2}$

$\Rightarrow 2 \cdot 3 \sqrt[4]{2}$

$\Rightarrow 6 \sqrt[4]{2}$

Part (b) Step 2. Conclusion

Hence, value of $(- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$ is $6 \sqrt[4]{2}$ .

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In the following exercises, simplify.
$(a) (5 \sqrt{6}) (- \sqrt{12}) (b) (- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$

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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In the following exercises, simplify.(a)56-12(b)-2184-94

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

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, simplify.
$(a) (5 \sqrt{6}) (- \sqrt{12}) (b) (- 2 \sqrt[4]{18}) (- \sqrt[4]{9})$