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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.97 (page 803)

Simplify:
$\frac{\sqrt{64 x^{4} y^{5}}}{\sqrt{2 x y^{3}}}$

Short Answer

Expert verified

The simplification of $\frac{\sqrt{64 x^{4} y^{5}}}{\sqrt{2 x y^{3}}}$ is $4 x y \sqrt{3 x}$

Step by step solution

01

Step 1. Given

An expression $\frac{\sqrt{64 x^{4} y^{5}}}{\sqrt{2 x y^{3}}}$

To simplify the expression

02

Step 2. Rewrite using the quotient property

Rewrite using the quotient property

$\frac{\sqrt{64 x^{4} y^{5}}}{\sqrt{2 x y^{3}}} = \sqrt{\frac{64 x^{4} y^{5}}{2 x y^{3}}}$

Remove the common factors.

$= \sqrt{48 x^{3} y^{2}}$

03

Step 3. Rewrite the radical as the product of two radicals.

$\frac{\sqrt{64 x^{4} y^{5}}}{\sqrt{2 x y^{3}}} = \sqrt{48 x^{3} y^{2}}$

$= \sqrt{16 x^{2} y^{2}} \sqrt{3 x}$

$= 4 x y \sqrt{3 x}$

The simplification of the expression is $4 x y \sqrt{3 x}$

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Most popular questions from this chapter

Simplify:

a. $\frac{m^{\frac{2}{3}} 路 m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ b. ${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}}$

In the following exercises, solve.
$\sqrt{s - 8} = s - 8$

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$ ,b. $\sqrt[5]{64}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{147}$

In the following exercises, solve.

$\sqrt{3 y - 4} = - 2$

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