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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. 221 (page 799)

Simplify:
$\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405}$

Short Answer

Expert verified

The value of the given expression is $- \sqrt[4]{5} .$

Step by step solution

01

Step 1. Given Information

The given expression is

$\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} .$

02

Step 2. Simplify the radicals

Like radicals can be added or subtracted so,

$\frac{1}{2} \sqrt[4]{80} - \frac{2}{3} \sqrt[4]{405} = \frac{1}{2} \sqrt[4]{16 路 5} - \frac{2}{3} \sqrt[4]{81 路 5} = \frac{1}{2} 路 \sqrt[4]{{(2)}^{4}} 路 \sqrt[4]{5} - \frac{2}{3} 路 \sqrt[4]{{(3)}^{4}} 路 \sqrt[4]{5} = \frac{1}{2} 路 2 路 \sqrt[4]{5} - \frac{2}{3} 路 3 路 \sqrt[4]{5} = \sqrt[4]{5} - 2 \sqrt[4]{5} = - \sqrt[4]{5}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}$

(b) $\sqrt[3]{\frac{5 x^{6} y^{9}}{40 x^{5} y^{3}}}$

(c) $\sqrt[4]{\frac{5 a^{8} b^{6}}{80 a^{3} b^{2}}}$

In the following exercises, simplify.

(a) $- 64^{\frac{3}{2}}$

(b) $- 64^{- \frac{3}{2}}$

(c) ${(- 64)}^{\frac{3}{2}}$

In the following exercises, solve.
$\sqrt{6 n + 1} + 4 = 8$

In the following exercises, simplify.

(a) $64^{\frac{5}{2}}$

(b) $81^{\frac{- 3}{2}}$

(c) ${(- 27)}^{\frac{2}{3}}$

In the following exercises, solve.
$\sqrt{u - 3} - 3 = u$

See all solutions

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