Chapter 8: Q. 89 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{100}{36}} b . \sqrt[3]{\frac{81}{375}} c . \sqrt[4]{\frac{1}{256}}$

Short Answer

Expert verified

The simplified expressions are,

$a . \frac{5}{3} b . \frac{3}{5} c . \frac{1}{4}$

Step by step solution

Step 1 Given expressions are,

$a . \sqrt{\frac{100}{36}} b . \sqrt[3]{\frac{81}{375}} c . \sqrt[4]{\frac{1}{256}}$

The objective is, we need to find the simplified expressions for the given expressions.

The quotient property is given by,

$\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ .

Part a Step 2 src="data:image/svg+xml;base64,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" localid="1645430757272" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/5eee5792-e664-42e4-a96f-0b47edb2710b.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220223%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220223T155613Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=118c2f38f09069172e70d3f0726abaf0dde506a9fa4770358460ff8801e52f49" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/5eee5792-e664-42e4-a96f-0b47edb2710b.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220221T080732Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=7a30c99e887d2a6a3c0c06faf07345921d0199d11b5a716398bd3be0c0fa4e9d" 10036

Now use the quotient property.

$\sqrt{\frac{100}{36}} = \frac{\sqrt{100}}{\sqrt{36}} = \frac{\sqrt{10 \times 10}}{\sqrt{6 \times 6}} = \frac{10}{6} = \frac{5}{3}$

Part b Step 2 813753

Now use the quotient property. $\sqrt[3]{\frac{81}{375}} = \frac{\sqrt[3]{81}}{\sqrt[3]{375}} = \frac{\sqrt[3]{3 \times 27}}{\sqrt[3]{3 \times 125}} = \frac{\sqrt[3]{3 \times 27}}{\sqrt[3]{3 \times 125}} = \frac{\sqrt[3]{27}}{\sqrt[3]{125}} = \frac{3}{5}$

Part c Step 2 12564 .

Now use the quotient property.

$\sqrt[4]{\frac{1}{256}} = \frac{\sqrt[4]{1}}{\sqrt[4]{256}} = \frac{\sqrt[4]{{(1)}^{4}}}{\sqrt[4]{{(4)}^{4}}} = \frac{1}{4}$

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In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{100}{36}} b . \sqrt[3]{\frac{81}{375}} c . \sqrt[4]{\frac{1}{256}}$

Short Answer

Step by step solution

Step 1 Given expressions are,

Part b Step 2 813753

Part c Step 2 12564 .

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In the following exercises, use the Quotient Property to simplify square roots.a.10036b.813753c.12564

Short Answer

Step by step solution

Step 1 Given expressions are,

Part b Step 2 813753

Part c Step 2 12564 .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{100}{36}} b . \sqrt[3]{\frac{81}{375}} c . \sqrt[4]{\frac{1}{256}}$