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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 689. (page 1151)

In the following exercises, simplify.
$\frac{\sqrt{20 y^{5}}}{\sqrt{2 y}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{20 y^{5}}}{\sqrt{2 y}}$ is, $y^{2} \sqrt{10}$ .

Step by step solution

01

Step1. Given information

Given expression is $\frac{\sqrt{20 y^{5}}}{\sqrt{2 y}}$ .

02

Step2. Rewrite

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

$\frac{\sqrt{20 y^{5}}}{\sqrt{2 y}} = \sqrt{\frac{20 y^{5}}{2 y}}$

03

Step3. Remove common factors in the numerator and denominator

$\sqrt{\frac{20 y^{5}}{2 y}} = \sqrt{\frac{2.10 . y^{4} . y}{2 . y}} = \sqrt{\frac{2 10 y^{4} y}{2 y}}$

04

Step4. Simplification

$\sqrt{\frac{2 10 y^{4} y}{2 y}} = \sqrt{10 y^{4}}$

05

Step5. Simplify the radical

$\sqrt{10 y^{4}} = y^{2} \sqrt{10}$

06

Step6. Check

$\frac{\sqrt{20 y^{5}}}{\sqrt{2 y}} = \sqrt{\frac{20 y^{5}}{2 y}} = \sqrt{\frac{2.10 . y^{4} . y}{2 . y}} = \sqrt{\frac{2 10 y^{4} y}{2 y}} = \sqrt{10 y^{4}} = y^{2} \sqrt{10}$

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