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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. 92 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{p^{20}}{p^{10}}} b . \sqrt[5]{\frac{d^{12}}{d^{7}}} c . \sqrt[8]{\frac{m^{12}}{m^{4}}}$

Short Answer

Expert verified

The simplified expressions are,

$a . |p^{5}| . b . |d| . c . |m| .$

Step by step solution

01

Step 1 Given expressions are,

$a . \sqrt{\frac{p^{20}}{p^{10}}} b . \sqrt[5]{\frac{d^{12}}{d^{7}}} c . \sqrt[8]{\frac{m^{12}}{m^{4}}}$

The objective is, we need to simplify the given expressions.

The quotient property to simplify under the radical is, $\frac{a^{m}}{a^{n}} = a^{m - n}$

02

Part a Step 2p20p10

Now use the quotient property.

$\sqrt{\frac{p^{20}}{p^{10}}} = \sqrt{p^{20 - 10}} = \sqrt{p^{10}} = |p^{5}|$

03

Part b Step 2 d12d75

Now use the quotient property.
$\sqrt[5]{\frac{d^{12}}{d^{7}}} = \sqrt[5]{d^{12 - 7}} = \sqrt[5]{d^{5}} = |d|$

04

Part c Step 2 m12m48

Now use the quotient property.
$\sqrt[8]{\frac{m^{12}}{m^{4}}} = \sqrt[8]{m^{12 - 4}} = \sqrt[8]{m^{8}} = |m|$

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed.

$\sqrt{y^{11}} \sqrt[3]{r^{5}} \sqrt[4]{s^{10}}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{28 q^{6}}{225}}$

In the following exercises, solve.

$\sqrt{2 n - 1} - 3 = 0$

Simplify:

$(a) \sqrt{180 m^{9} n^{11}} (b) \sqrt{72 x^{6} y^{5}} (c) \sqrt{80 x^{7} y^{4}} .$

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

See all solutions

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