Chapter 8: Q. 593 (page 857)

In the following exercises, simplify. Assume all variables are positive.
$\frac{\sqrt{245 x y^{- 4}}}{\sqrt{45 x^{- 4} y^{3}}}$

Short Answer

Expert verified

The simplified expression is $\frac{7 x^{3}}{3 y} \times \sqrt{\frac{x}{y}}$

Step by step solution

Step 1. Given Information

We have $\frac{\sqrt{245 x y^{- 4}}}{\sqrt{45 x^{- 4} y^{3}}}$

Step 2. Factor the Radicand

$\frac{\sqrt{245 x y^{- 4}}}{\sqrt{45 x^{- 4} y^{3}}} = \frac{\sqrt{5 \times 7 \times 7 \times x \times x^{4}}}{\sqrt{3 \times 3 \times 5 \times y^{3} \times y^{4}}} = \frac{7 x^{2} \sqrt{5} \sqrt{x}}{3 \times y \times y^{2} \sqrt{5} \sqrt{y}}$

Step 3. Simplify the expression

$\frac{7 x^{2}}{3 y} \times \frac{\sqrt{5}}{\sqrt{5}} \times \sqrt{\frac{x}{y}} = \frac{7 x^{3}}{3 y} \times \sqrt{\frac{x}{y}}$

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In the following exercises, simplify. Assume all variables are positive.
$\frac{\sqrt{245 x y^{- 4}}}{\sqrt{45 x^{- 4} y^{3}}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the Radicand

Step 3. Simplify the expression

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In the following exercises, simplify. Assume all variables are positive.245xy-445x-4y3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factor the Radicand

Step 3. Simplify the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Decision Maths

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify. Assume all variables are positive.
$\frac{\sqrt{245 x y^{- 4}}}{\sqrt{45 x^{- 4} y^{3}}}$