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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. 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

01

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

02

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}}|

03

Part b Step 2 r14r53

Now use the quotient property.

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

04

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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Most popular questions from this chapter

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

Explain what is meant by the $n^{t h}$ root of a number.

In the following exercises, write with a rational exponent.

$鈸� \sqrt[8]{r} 鈸� \sqrt[10]{s} 鈸� \sqrt[4]{t}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

(c) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

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