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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. 98 (page 772)

Use the Quotient Property to simplify square roots.
$\sqrt{\frac{125 n^{7}}{169}}$

Short Answer

Expert verified

The simplified form is $\frac{5 |n^{5}| \sqrt{5 n}}{13}$ .

Step by step solution

01

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{125 n^{7}}{169}}$ .

02

Step 2. Write the concept.

To determine a 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, localid="1644695115626" $b 鈮� 0$ for any integer $n 鈮� 2$ .

03

Step 3. Calculation.

Simplifying the expression.

$\sqrt{\frac{125 n^{7}}{169}} = \sqrt{\frac{25 n^{6} . 5 n}{169}} = \frac{\sqrt{25 n^{6} . 5 n}}{\sqrt{169}} = \frac{\sqrt{{(5 n^{5})}^{2}} . \sqrt{5 n}}{13} = \frac{5 |n^{5}| \sqrt{5 n}}{13}$

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Most popular questions from this chapter

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

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

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

Simplify:

$(a) 2 + \sqrt{98} (b) \frac{6 - \sqrt{45}}{3} .$

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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