Chapter 8: Q. 76 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

Short Answer

Expert verified

The expression on simplification is $4 | r s | \sqrt{6 r s}, 2 x^{2} y^{2} \sqrt[3]{10 x}, 2 x^{2} y^{2} \sqrt[4]{5 y}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

Using the product property

Using the product property, we get

$\sqrt{96 r^{3} s^{3}} = \sqrt{16 r^{2} s^{2} \cdot 6 r s} \sqrt{96 r^{3} s^{3}} = \sqrt{(4 r s)^{2} \cdot 6 r s} \sqrt{96 r^{3} s^{3}} = \sqrt{(4 r s)^{2}} \cdot \sqrt{6 r s} \sqrt{96 r^{3} s^{3}} = 4 | r s | \sqrt{6 r s}$

Using the product property

Using the property, we get

$\sqrt[3]{80 x^{7} y^{6}} = \sqrt[3]{8 x^{6} y^{6} \cdot 10 x} \sqrt[3]{80 x^{7} y^{6}} = \sqrt[3]{{(2 x^{2} y^{2})}^{3} \cdot 10 x} \sqrt[3]{80 x^{7} y^{6}} = \sqrt[3]{{(2 x^{2} y^{2})}^{3}} \cdot \sqrt[3]{10 x} \sqrt[3]{80 x^{7} y^{6}} = 2 x^{2} y^{2} \sqrt[3]{10 x}$

Using the product property

Using the property, we get

$\sqrt[4]{80 x^{8} y^{9}} = \sqrt[4]{16 x^{8} y^{8} \cdot 5 y} \sqrt[4]{80 x^{8} y^{9}} = \sqrt[4]{{(2 x^{2} y^{2})}^{4} \cdot 5 y} \sqrt[4]{80 x^{8} y^{9}} = \sqrt[4]{{(2 x^{2} y^{2})}^{4}} \cdot \sqrt[4]{5 y} \sqrt[4]{80 x^{8} y^{9}} = 2 |x^{2} y^{2}| \sqrt[4]{5 y} \sqrt[4]{80 x^{8} y^{9}} = 2 x^{2} y^{2} \sqrt[4]{5 y}$

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

Short Answer

Step by step solution

Given information

Using the product property

Using the product property

Using the product property

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In the following exercises, simplify using absolute value signs as needed.96r3s3,80x7y63,80x8y94

Short Answer

Step by step solution

Given information

Using the product property

Using the product property

Using the product property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$