Chapter 8: Q. 8.99 (page 804)

Simplify:
(a) $\frac{5}{\sqrt{3}}$
(b) $\sqrt{\frac{3}{32}}$
(c) $\frac{2}{\sqrt{2 x}}$

Short Answer

Expert verified

The simplification of $\frac{5}{\sqrt{3}}$ is $\frac{5 \sqrt{3}}{3}$

The simplification of $\sqrt{\frac{3}{32}}$ is $\frac{\sqrt{6}}{8}$

The simplification of $\frac{2}{\sqrt{2 x}}$ is $\frac{\sqrt{2 x}}{x}$

Step by step solution

Part (a) Step 1. Given

An expression $\frac{5}{\sqrt{3}}$

To simplify the expression

Step 2. Multiply numerator and denominator by the same factor

Multiply numerator and denominator by $\sqrt{3}$

$\frac{5}{\sqrt{3}} = \frac{5 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$

$= \frac{5 \sqrt{3}}{3}$

Part (b) Step 1. Given

An expression $\sqrt{\frac{3}{32}}$

To simplify the expression

Part (a) Step 2. Rewrite using the quotient property

The expression is not a perfect square, so rewrite using quotient property.

$\sqrt{\frac{3}{32}} = \frac{\sqrt{3}}{\sqrt{32}}$

$= \frac{\sqrt{3}}{\sqrt{16} . \sqrt{2}}$

Step 3. Simplify the expression

$\sqrt{\frac{3}{32}} = \frac{\sqrt{3}}{4 \sqrt{2}}$

Multiply numerator and denominator by $\sqrt{2}$ ,

$= \frac{\sqrt{3} . \sqrt{2}}{4 \sqrt{2} . \sqrt{2}}$

$= \frac{\sqrt{6}}{8}$

The simplification of the expression is $\frac{\sqrt{6}}{8}$

Part (c) Step 1. Given

An expression $\frac{2}{\sqrt{2 x}}$

To simplify the expression

Part (c) Step 2. Multiply numerator and denominator by the same factor

Multiply the numerator and denominator by $\sqrt{2 x}$

$\frac{2}{\sqrt{2 x}} = \frac{2 \sqrt{2 x}}{\sqrt{2 x} \sqrt{2 x}}$

Simplify the expression

$= \frac{2 \sqrt{2 x}}{2 x}$

$= \frac{\sqrt{2 x}}{x}$

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

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Simplify:
(a) $\frac{5}{\sqrt{3}}$
(b) $\sqrt{\frac{3}{32}}$
(c) $\frac{2}{\sqrt{2 x}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Step 2. Multiply numerator and denominator by the same factor

Part (b) Step 1. Given

Part (a) Step 2. Rewrite using the quotient property

Step 3. Simplify the expression

Part (c) Step 1. Given

Part (c) Step 2. Multiply numerator and denominator by the same factor

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Simplify:(a)53(b) 332(c) 22x

Short Answer

Step by step solution

Part (a) Step 1. Given

Step 2. Multiply numerator and denominator by the same factor

Part (b) Step 1. Given

Part (a) Step 2. Rewrite using the quotient property

Step 3. Simplify the expression

Part (c) Step 1. Given

Part (c) Step 2. Multiply numerator and denominator by the same factor

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

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Logic and Functions

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Simplify:
(a) $\frac{5}{\sqrt{3}}$
(b) $\sqrt{\frac{3}{32}}$
(c) $\frac{2}{\sqrt{2 x}}$