Chapter 8: Q. 8.94 (page 801)

Simplify:
(a) $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$
(b) $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$ is $\frac{5 q^{2}}{6}$

The simplification of $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$ is $\frac{2}{b}$

Step by step solution

Part (a) Step 1. Given

An expression $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$

To simplify the expression.

Part (a) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}} = \sqrt{\frac{75 q^{5}}{108 q}}$

Remove the common factor

$= \sqrt{\frac{25 q^{4}}{36}}$

Part (a) Step 3. Simplify the expression

$\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}} = \sqrt{\frac{25 q^{4}}{36}}$

$= \frac{5 q^{2}}{6}$

The simplification of the expression is $\frac{5 q^{2}}{6}$

Part (b) Step 1. Given

An expression $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$

To simplify the expression.

Part (b) Step 2. Rewrite using quotient property

Rewrite using quotient property

$\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}} = \sqrt[3]{\frac{72 b^{2}}{9 b^{5}}}$

Remove the common factors.

$= \sqrt[3]{\frac{8}{b^{3}}}$

Part (b) Step 3. Simplify the expression

$\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}} = \sqrt[3]{\frac{2^{3}}{b^{3}}}$

$= \frac{2}{b}$

The simplification of the expression is $\frac{2}{b}$

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Simplify:
(a) $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$
(b) $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite using quotient property

Part (a) Step 3. Simplify the expression

Part (b) Step 1. Given

Part (b) Step 2. Rewrite using quotient property

Part (b) Step 3. Simplify the expression

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Simplify:(a)75q5108q(b) 72b239b53

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite using quotient property

Part (a) Step 3. Simplify the expression

Part (b) Step 1. Given

Part (b) Step 2. Rewrite using quotient property

Part (b) Step 3. Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Simplify:
(a) $\frac{\sqrt{75 q^{5}}}{\sqrt{108 q}}$
(b) $\frac{\sqrt[3]{72 b^{2}}}{\sqrt[3]{9 b^{5}}}$