Q. 8.79 Simplify:(32)(220)(2183)(-363)... [FREE SOLUTION]

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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. 8.79 (page 792)

Simplify:
$(3 \sqrt{2}) (2 \sqrt{20})$
$(2 \sqrt[3]{18}) (- 3 \sqrt[3]{6})$

Short Answer

Expert verified

Part a. $12 \sqrt{10}$

Part b. $- 18 \sqrt[3]{4}$

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} 路 \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

$\begin{array}{rcl} (3 \sqrt{2}) (2 \sqrt{20}) & = & (3 路 2) (\sqrt{2} 路 \sqrt{20}) \\ = & 6 \sqrt{2 路 20} \\ = & 6 \sqrt{40} \end{array}$

Now, the radical can be simplified as

$\begin{array}{rcl} 6 \sqrt{40} & = & 6 \sqrt{4 路 10} \\ = & 6 \sqrt{4} 路 \sqrt{10} \\ = & 6 路 2 路 \sqrt{10} \\ = & 12 \sqrt{10} \end{array}$

Part (b) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} 路 \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

localid="1645682272556" $\begin{array}{rcl} (2 \sqrt[3]{18}) (- 3 \sqrt[3]{6}) & = & 2 路 (- 3) 路 (\sqrt[3]{18} 路 \sqrt[3]{6}) \\ = & - 6 \sqrt[3]{18 路 6} \\ = & - 6 \sqrt[3]{108} \end{array}$

Now, the radical can be simplified as

localid="1645682314593" $\begin{array}{rcl} - 6 \sqrt[3]{108} & = & - 6 \sqrt[3]{27 路 4} \\ = & - 6 路 \sqrt[3]{27} 路 \sqrt[3]{4} \\ = & - 6 路 3 路 \sqrt[3]{4} \\ = & - 18 \sqrt[3]{4} \end{array}$

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91影视

Simplify:
$(3 \sqrt{2}) (2 \sqrt{20})$
$(2 \sqrt[3]{18}) (- 3 \sqrt[3]{6})$

Short Answer

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Part (b) Step 1. Multiply the radicals and simplify

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