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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. 8.84 (page 794)

Simplify:
$\sqrt{8} (2 - 5 \sqrt{8})$
$\sqrt[3]{3} (- \sqrt[3]{9} - \sqrt[3]{6})$

Short Answer

Expert verified

Part a. $\begin{array}{rcl} 2 \sqrt{8} - 40 \end{array}$

Part b. $- 3 - \sqrt[3]{18}$

Step by step solution

01

Part (a) Step 1. Expand the expression and simplify the radicals

First, expand the expression using the distributive property.

$\begin{array}{rcl} \sqrt{8} (2 - 5 \sqrt{8}) & = & \sqrt{8} 路 2 - \sqrt{8} 路 5 \sqrt{8} \\ = & 2 \sqrt{8} - 5 {(\sqrt{8})}^{2} = 2 \sqrt{8} - 5 路 8 \\ = & 2 \sqrt{8} - 40 \end{array}$

There are no like radicals, so the expression cannot be simplified further.

02

Part (b) Step 1. Expand the expression and simplify the radicals

First, expand the expression using the distributive property.

$\begin{array}{rcl} \sqrt[3]{3} (- \sqrt[3]{9} - \sqrt[3]{6}) & = & \sqrt[3]{3} 路 (- \sqrt[3]{9}) - \sqrt[3]{3} 路 \sqrt[3]{6} \\ = & - \sqrt[3]{3 路 9} - \sqrt[3]{3 路 6} \\ = & - \sqrt[3]{27} - \sqrt[3]{18} \\ = & - 3 - \sqrt[3]{18} \end{array}$

There are no like radicals, so the expression cannot be simplified further.

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Most popular questions from this chapter

Simplify $\sqrt{45}$

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$ ,b. $\sqrt[5]{64}$

Simplify:

(a) $4^{\frac{3}{2}}$

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

(c) $625^{- \frac{3}{4}}$

In the following exercises, solve.

$\sqrt{5 v - 2} + 5 = 0$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{80} .$

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