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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. 334 (page 1090)

Simplify Expressions -
$\frac{\sqrt{98 r s^{10}}}{\sqrt{2 r^{3} s^{4}}}$

Short Answer

Expert verified

The simplification of Expression will be - $\frac{7 s^{3}}{r}$

Step by step solution

01

Step 1. Given Data

Expressions -

$\frac{\sqrt{98 r s^{10}}}{\sqrt{2 r^{3} s^{4}}}$

02

Step 2. To Find

Simplify The Expressions.

03

Step 3. Explanation

Expressions - $\frac{\sqrt{98 r s^{10}}}{\sqrt{2 r^{3} s^{4}}}$

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

localid="1648573311567" $\frac{\sqrt{98 r s^{10}}}{\sqrt{2 r^{3} s^{4}}} \sqrt{\frac{98 r s^{10}}{2 r^{3} s^{4}}}$

04

Step 4. Calculation

Remove common factors in the numerator and denominator.

$\sqrt{\frac{98 r s^{10}}{2 r^{3} s^{4}}} \sqrt{\frac{2 脳 49 脳 r 脳 s^{4} 脳 s^{6}}{2 脳 r 脳 r^{2} 脳 s^{4}}} \sqrt{\frac{49 s^{6}}{r^{2}}}$

Simplify -

$\sqrt{\frac{49 s^{6}}{r^{2}}} \frac{7 s^{3}}{r}$

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