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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q582 (page 857)

Simplify using absolute values as necessary.
$\sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}}$

Short Answer

Expert verified

The Solution is $\frac{y}{2 x}$

Step by step solution

01

The Given Information

An expression is $\sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}}$

02

Simplifying

$= \sqrt{\frac{45 x^{3} y^{4}}{180 x^{5} y^{2}}} 45 \times 4 = 180 \frac{x^{3}}{x^{5}} = \frac{1}{x^{2}} \frac{y^{4}}{y^{2}} = \frac{y^{2}}{1} = \sqrt{\frac{y^{2}}{4 x^{2}}} = \frac{y}{2 x}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98 r^{5}}{100}}$

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[5]{64}$ , b. $\sqrt[3]{256}$

Simplify:

a. $\frac{m^{\frac{2}{3}} \cdot m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ 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, write with a rational exponent.

$\sqrt[3]{7 c} ⓑ \sqrt[7]{12 d} ⓒ 2 \sqrt[4]{6 b}$

Simplify:

$(a) \sqrt{\frac{98}{162}} (b) \sqrt[3]{\frac{24}{375}} (c) \sqrt[4]{\frac{4}{324}}$

See all solutions

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