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

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, $\sqrt[n]{a^{n}} = a$ .

Part a Step 2 y4y8

Now use the quotient property.

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

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}

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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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

Step by step solution

Step 1 Given expressions are,

Part a Step 2 y4y8

Part b Step 2 u21u115

Part c Step 2 v30v126

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In the following exercises, use the Quotient Property to simplify square roots.a.y4y8b.u21u115c.v30v126

Short Answer

Step by step solution

Step 1 Given expressions are,

Part a Step 2 y4y8

Part b Step 2 u21u115

Part c Step 2 v30v126

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

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