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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. 93 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{y^{4}}{y^{8}}} b . \sqrt[5]{\frac{u^{21}}{u^{11}}} c . \sqrt[6]{\frac{v^{30}}{v^{12}}}$

Short Answer

Expert verified

The simplified expressions are,

$a . \frac{1}{y^{2}} b . u^{2} c . |v^{3}|$

Step by step solution

01

Step 1 Given expressions are,

$a . \sqrt{\frac{y^{4}}{y^{8}}} b . \sqrt[5]{\frac{u^{21}}{u^{11}}} c . \sqrt[6]{\frac{v^{30}}{v^{12}}}$

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

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

Also, we know that, $\sqrt[n]{a^{n}} = a$ .

02

Part a Step 2 y4y8

Now use the quotient property.

$\sqrt{\frac{y^{4}}{y^{8}}} = \sqrt{y^{4 - 8}} = \sqrt{y^{- 4}} = \sqrt{\frac{1}{y^{4}}} = \frac{1}{y^{2}}$

03

Part b Step 2 u21u115

Now use the quotient property.

\sqrt[5]{\frac{u^{21}}{u^{11}}} = \sqrt[5]{u^{21 - 11}} = \sqrt[5]{u^{10}} = u^{2}

04

Part c Step 2 v30v126

Now use the quotient property.

\sqrt[6]{\frac{v^{30}}{v^{12}}} = \sqrt[6]{v^{30 - 12}} = \sqrt[6]{v^{18}} = |v^{3}|

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Most popular questions from this chapter

Simplify:

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

Simplify::
(a) $100^{\frac{1}{2}}$

(b) $27^{\frac{1}{3}}$

(c) $81^{\frac{1}{4}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

In the following exercises, use the Product Property to simplify radical expressions a $\sqrt[4]{3125}$ , b. $\sqrt[3]{81}$

In the following exercises, solve.
$\sqrt{6 n + 1} + 4 = 8$

See all solutions

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