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

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, $\frac{a^{m}}{a^{n}} = a^{m - n}$

Part a Step 2p20p10

Now use the quotient property.

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

Part b Step 2 d12d75

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

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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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

Step by step solution

Step 1 Given expressions are,

Part a Step 2p20p10

Part b Step 2 d12d75

Part c Step 2 m12m48

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In the following exercises, use the Quotient Property to simplify square roots.a.p20p10b.d12d75c.m12m48

Short Answer

Step by step solution

Step 1 Given expressions are,

Part a Step 2p20p10

Part b Step 2 d12d75

Part c Step 2 m12m48

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Probability and Statistics

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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