Chapter 8: Q. 8.81 (page 793)

Simplify:
$(6 \sqrt{6 x^{2}}) (8 \sqrt{30 x^{4}})$
$(- 4 \sqrt[4]{12 y^{3}}) (- \sqrt[4]{8 y^{3}})$

Short Answer

Expert verified

Part a. $288 x^{3} \sqrt{5}$

Part b. $\begin{array}{rcl} 8 y \sqrt[4]{6 y^{2}} \end{array}$

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

$\begin{array}{rcl} (6 \sqrt{6 x^{2}}) (8 \sqrt{30 x^{4}}) & = & 6 \cdot 8 \cdot \sqrt{6 x^{2} \cdot 30 x^{4}} \\ = & 48 \sqrt{180 x^{6}} \end{array}$

Now, the radical can be simplified as

$\begin{array}{rcl} 48 \sqrt{180 x^{6}} & = & 48 \sqrt{36 x^{6} \cdot 5} \\ = & 48 \sqrt{36 x^{6}} \cdot \sqrt{5} \\ = & 48 \cdot 6 x^{3} \sqrt{5} \\ = & 288 x^{3} \sqrt{5} \end{array}$

Part (b) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

$\begin{array}{rcl} (- 4 \sqrt[4]{12 y^{3}}) (- \sqrt[4]{8 y^{3}}) & = & (- 4) (- 1) (\sqrt[4]{12 y^{3}} \cdot \sqrt[4]{8 y^{3}}) \\ = & 4 \sqrt[4]{12 y^{3} \cdot 8 y^{3}} \\ = & 4 \sqrt[4]{96 y^{6}} \end{array}$

Now, the radical can be simplified as

$\begin{array}{rcl} 4 \sqrt[4]{96 y^{6}} & = & 4 \sqrt[4]{16 y^{4} \cdot 6 y^{2}} \\ = & 4 \cdot \sqrt[4]{16 y^{4}} \cdot \sqrt[4]{6 y^{2}} \\ = & 4 \cdot 2 y \sqrt[4]{6 y^{2}} \\ = & 8 y \sqrt[4]{6 y^{2}} \end{array}$

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Simplify:
$(6 \sqrt{6 x^{2}}) (8 \sqrt{30 x^{4}})$
$(- 4 \sqrt[4]{12 y^{3}}) (- \sqrt[4]{8 y^{3}})$

Short Answer

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Part (b) Step 1. Multiply the radicals and simplify

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Simplify:(66x2)(830x4)(-412y34)(-8y34)

Short Answer

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Part (b) Step 1. Multiply the radicals and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Simplify:
$(6 \sqrt{6 x^{2}}) (8 \sqrt{30 x^{4}})$
$(- 4 \sqrt[4]{12 y^{3}}) (- \sqrt[4]{8 y^{3}})$