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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. 97 (page 772)

In the following exercises, use the Quotient Property to simplify square roots.
$\sqrt{\frac{300 m^{5}}{64}}$

Short Answer

Expert verified

The simplified expression is, $\frac{10 m^{2} . \sqrt{3 m}}{8}$ .

Step by step solution

01

Step 1 Given expression is,

$\sqrt{\frac{300 m^{5}}{64}}$

The objective is, we need to simplify the given expression.

The quotient property is given by,

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

Also we know that, $\sqrt[n]{a^{n}} = |a|$ .

02

Step 2 Simplify the given expression.

$\sqrt{\frac{300 m^{5}}{64}} = \sqrt{\frac{100 m^{4} 脳 3 m}{64}} = \sqrt{\frac{{(10 m^{2})}^{2} 脳 3 m}{{(8)}^{2}}}$

Now use the quotient property.

$\sqrt{\frac{300 m^{5}}{64}} = \frac{\sqrt{{(10 m^{2})}^{2} 脳 3 m}}{\sqrt{{(8)}^{2}}} = \frac{10 m^{2} . \sqrt{3 m}}{8}$

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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.

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