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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. 336 (page 1090)

Simplify Expressions -
$\frac{\sqrt{810 c^{3} d^{7}}}{\sqrt{1000 c^{5} d}}$

Short Answer

Expert verified

The simplification of Expression will be - $\frac{9 d^{3}}{10 c}$

Step by step solution

01

Step 1. Given Data

Expressions -

$\frac{\sqrt{810 c^{3} d^{7}}}{\sqrt{1000 c^{5} d}}$

02

Step 2. To Find

Simplify The Expressions

03

Step 3. Explanation

Expressions - $\frac{\sqrt{810 c^{3} d^{7}}}{\sqrt{1000 c^{5} d}}$

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

$\frac{\sqrt{810 c^{3} d^{7}}}{\sqrt{1000 c^{5} d}} \sqrt{\frac{810 c^{3} d^{7}}{1000 c^{5} d}}$

04

Step 4. Calculation

Remove common factors in the numerator and denominator.

$\sqrt{\frac{810 c^{3} d^{7}}{1000 c^{5} d}} \sqrt{\frac{81 脳 10 脳 c^{3} 脳 d^{6} 脳 d}{100 脳 10 脳 c^{3} 脳 c^{2} 脳 d}} \sqrt{\frac{81 d^{6}}{100 c^{2}}}$

simplify-

$\sqrt{\frac{81 d^{6}}{100 c^{2}}} \frac{9 d^{3}}{10 c}$

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In the following exercises, simplify and rationalize the denominator.

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