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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q.335 (page 1090)

Simplify Expressions -
$\frac{\sqrt{320 m n^{5}}}{\sqrt{45 m^{7} n^{3}}}$

Short Answer

Expert verified

The simplification of Expression will be - $\frac{8 n}{3 m^{3}}$

Step by step solution

01

Step 1. Given Data

Expressions -

$\frac{\sqrt{320 m n^{5}}}{\sqrt{45 m^{7} n^{3}}}$

02

Step 2. To Find

Simplify The Expressions

03

Step 3. Explanation

Expressions - $\frac{\sqrt{320 m n^{5}}}{\sqrt{45 m^{7} n^{3}}}$

Neither radicand is a perfect square, so rewrite using the quotient property of square roots -

$\frac{\sqrt{320 m n^{5}}}{\sqrt{45 m^{7} n^{3}}} \sqrt{\frac{320 m n^{5}}{45 m^{7} n^{3}}}$

04

Step 4. Calculation

Remove common factors in the numerator and denominator.

$\sqrt{\frac{320 m n^{5}}{45 m^{7} n^{3}}} \sqrt{\frac{64 脳 5 脳 m 脳 n^{3} 脳 n^{2}}{5 脳 9 脳 m 脳 m^{6} 脳 n^{3}}} \sqrt{\frac{64 n^{2}}{9 m^{6}}}$

simplify-

$\sqrt{\frac{64 n^{2}}{9 m^{6}}} \frac{8 n}{3 m^{3}}$

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Most popular questions from this chapter

In the following exercises, simplify by rationalizing the denominator

$\frac{\sqrt{3}}{\sqrt{m} - \sqrt{5}}$

In the following exercises, simplify and rationalize the denominator.

$- \frac{9}{2 \sqrt{3}}$

In the following exercises, solve.

$\sqrt{6 n + 1} + 4 = 8$ .

In the following exercises, solve.

$\sqrt{8 u + 1} + 9 = 0$

Try It.

A helicopter dropped a rescue package from a height of $1, 296$ feet. Use the formula role="math" localid="1647883430342" $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

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