Chapter 8: Q. 94 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{q^{8}}{q^{14}}} b . \sqrt[3]{\frac{r^{14}}{r^{5}}} c . \sqrt[4]{\frac{c^{21}}{c^{9}}}$

Short Answer

Expert verified

The simplified expressions are,

$a . |\frac{1}{q^{3}}| b . |r^{3}| c . |c^{3}|$

Step by step solution

Step 1 Given expressions are,

$a . \sqrt{\frac{q^{8}}{q^{14}}} b . \sqrt[3]{\frac{r^{14}}{r^{5}}} c . \sqrt[4]{\frac{c^{21}}{c^{9}}}$

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 q8q14

Now use the quotient property.

\sqrt{\frac{q^{8}}{q^{14}}} = \sqrt{q^{8 - 14}} = \sqrt{q^{- 6}} = \sqrt{\frac{1}{q^{6}}} = |\frac{1}{q^{3}}|

Part b Step 2 r14r53

Now use the quotient property.

$\sqrt[3]{\frac{r^{14}}{r^{5}}} = \sqrt[3]{r^{14 - 5}} = \sqrt[3]{r^{9}} = \sqrt[3]{{(r^{3})}^{3}} = |r^{3}|$

Part c Step 2 c21c94

Now use the quotient property.

\sqrt[4]{\frac{c^{21}}{c^{9}}} = \sqrt[4]{c^{21 - 9}} = \sqrt[4]{c^{12}} = \sqrt[4]{{(c^{3})}^{4}} = |c^{3}|

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In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{q^{8}}{q^{14}}} b . \sqrt[3]{\frac{r^{14}}{r^{5}}} c . \sqrt[4]{\frac{c^{21}}{c^{9}}}$

Short Answer

Step by step solution

Step 1 Given expressions are,

Part a Step 2 q8q14

Part b Step 2 r14r53

Part c Step 2 c21c94

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In the following exercises, use the Quotient Property to simplify square roots.a.q8q14b.r14r53c.c21c94

Short Answer

Step by step solution

Step 1 Given expressions are,

Part a Step 2 q8q14

Part b Step 2 r14r53

Part c Step 2 c21c94

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Quotient Property to simplify square roots.
$a . \sqrt{\frac{q^{8}}{q^{14}}} b . \sqrt[3]{\frac{r^{14}}{r^{5}}} c . \sqrt[4]{\frac{c^{21}}{c^{9}}}$