Chapter 8: Q. 8.98 (page 802)

Simplify:
$\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}}$ is $4 a b \sqrt{3 b}$

Step by step solution

Step 1. Given

An expression $\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}}$

To simplify the expression

Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}} = \sqrt{\frac{96 a^{5} b^{4}}{2 a^{3} b}}$

Remove the common factors.

$= \sqrt{48 a^{2} b^{3}}$

Step 3. Rewrite the radical as the product of two radicals.

$\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}} = \sqrt{48 a^{2} b^{3}}$

$= \sqrt{16 a^{2} b^{2}} . \sqrt{3 b}$

$= 4 a b \sqrt{3 b}$

The simplification of the expression is $4 a b \sqrt{3 b}$

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Simplify:
$\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Rewrite using the quotient property

Step 3. Rewrite the radical as the product of two radicals.

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Simplify:96a5b42a3b

Short Answer

Step by step solution

Step 1. Given

Step 2. Rewrite using the quotient property

Step 3. Rewrite the radical as the product of two radicals.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
$\frac{\sqrt{96 a^{5} b^{4}}}{\sqrt{2 a^{3} b}}$