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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. 8.49 (page 770)

Simplify:
$(a) \frac{\sqrt{98 z^{5}}}{\sqrt{2 z}} (b) \frac{\sqrt[3]{- 500}}{\sqrt[3]{2}} (c) \frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $7 z^{2} .$

Part b. After simplifying we get, $- 5 \sqrt[3]{2} .$

Part c. After simplifying we get, $3 m \sqrt[4]{2 m^{2}} .$

Step by step solution

01

Part a Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt{98 z^{5}}}{\sqrt{2 z}}$

By using the property we can write as $\sqrt{\frac{98 z^{5}}{2 z}} .$

02

Part a Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt{\frac{98 z^{5}}{2 z}} = \sqrt{49 z^{5 - 1}} = \sqrt{{(7 z^{2})}^{2}} = 7 z^{2}$

03

Part b Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[3]{- 500}}{\sqrt[3]{2}}$

By using the property we can write as $\sqrt[3]{\frac{- 500}{2}} .$

04

Part b Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[3]{\frac{- 500}{2}} = \sqrt[3]{- 250} = \sqrt[3]{(- 5^{3}) 路 2} = - 5 \sqrt[3]{2}$

05

Part c Step 1. Use the Quotient property to write as one radical

Given: $\frac{\sqrt[4]{486 m^{11}}}{\sqrt[4]{3 m^{5}}}$

By using the property we can write as $\sqrt[4]{\frac{486 m^{11}}{3 m^{5}}} .$

06

Part c Step 2: Simplify the fraction under the radical

By simplifying we get,

$\sqrt[4]{\frac{486 m^{11}}{3 m^{5}}} = \sqrt[4]{162 m^{6}} = \sqrt[4]{{(3 m)}^{4}} 路 \sqrt[4]{2 m^{2}} = 3 m \sqrt[4]{2 m^{2}}$

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Most popular questions from this chapter

In the following exercises, simplify.

(a) $25^{\frac{3}{2}}$

(b) $9^{\frac{- 3}{2}}$

(c) ${(- 64)}^{\frac{2}{3}}$

In the following exercises, solve.

$\sqrt[3]{2 x} = - 2$

In the following exercises, solve.
$\sqrt{u - 3} - 3 = u$

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

In the following exercises, write with a rational exponent.

$鈸� \sqrt[7]{x} 鈸� \sqrt[9]{y} 鈸� \sqrt[5]{f}$

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