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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. 99 (page 772)

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{98 r^{5}}{100}}$

Short Answer

Expert verified

The simplified form is $\frac{7 r^{2} \sqrt{2 r}}{10}$ .

Step by step solution

01

Step 1. Given information.

The radical expression as:

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

02

Step 2. Write the concept.

To determine simplified form of a radical expression following formula is used:

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} a n d \frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$

if $\sqrt[n]{a} a n d \sqrt[n]{b}$ are real numbers, $b 鈮� 0$ for any integer

$n 鈮� 2$ .

.

03

Step 3. Calculation.

Simplifying the expression.

$\sqrt{\frac{98 r^{5}}{100}} = \sqrt{\frac{49 r^{4} . 2 r}{100}} = \frac{\sqrt{49 r^{4} . 2 r}}{\sqrt{100}} = \frac{\sqrt{{(7 r^{2})}^{2} .} \sqrt{2 r}}{10} = \frac{7 |r^{2}| \sqrt{2 r}}{10} = \frac{7 r^{2} \sqrt{2 r}}{10}$

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Most popular questions from this chapter

In the following exercises, simplify.

(a) $100^{\frac{3}{2}}$

(b) $49^{- \frac{5}{2}}$

(c) ${(- 100)}^{\frac{3}{2}}$

Simplify $\sqrt{45}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

In the following exercises, simplify.

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

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

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

In the following exercises, use the Product Property to simplify radical expression $\sqrt{80} .$

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