Chapter 8: Q. 77 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Short Answer

Expert verified

The expression in simplified form is $8 |q r^{3}| \sqrt{3 q r}, 3 m^{3} n^{3} \sqrt[3]{2 n}, 3 a^{2} b^{2} \sqrt[4]{a}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Using the product property

Using the property, we get

$\sqrt{192 q^{3} r^{7}} = \sqrt{64 q^{2} r^{6} \cdot 3 q r} \sqrt{192 q^{3} r^{7}} = \sqrt{{(8 q r^{3})}^{2} \cdot 3 q r} \sqrt{192 q^{3} r^{7}} = \sqrt{{(8 q r^{3})}^{2}} \cdot \sqrt{3 q r} \sqrt{192 q^{3} r^{7}} = 8 |q r^{3}| \sqrt{3 q r}$

Using the product property

Using the property, we get

$\sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{27 m^{9} n^{9} \cdot 2 n} \sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{{(3 m^{3} n^{3})}^{3} \cdot 2 n} \sqrt[3]{54 m^{9} n^{10}} = \sqrt[3]{{(3 m^{3} n^{3})}^{3}} \cdot \sqrt[3]{2 n} \sqrt[3]{54 m^{9} n^{10}} = 3 m^{3} n^{3 .} \sqrt[3]{2 n}$

Using the product property

Using the property, we get

$\sqrt[4]{81 a^{9} b^{8}} = \sqrt[4]{81 a^{8} b^{8} \cdot a} \sqrt[4]{81 a^{9} b^{8}} = \sqrt[4]{{(3 a^{2} b^{2})}^{4} \cdot a} \sqrt[4]{81 a^{9} b^{8}} = = \sqrt[4]{{(3 a^{2} b^{2})}^{4}} \cdot \sqrt[4]{a} \sqrt[4]{81 a^{9} b^{8}} = 3 |a^{2} b^{2}| . \sqrt[4]{a} \sqrt[4]{81 a^{9} b^{8}} = 3 a^{2} b^{2} . \sqrt[4]{a}$

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

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.192q3r7,54m9n103,81a9b84

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

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$