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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. 208 (page 798)

In the following exercises, multiply:
$(a) {(5 - \sqrt{10})}^{2} (b) {(8 + 3 \sqrt{2})}^{2}$

Short Answer

Expert verified

Part a. By multiplying we get, $35 - 10 \sqrt{10} .$

Part b. By multiplying we get, $82 + 48 \sqrt{2} .$

Step by step solution

01

Part a Step 1. Multiply the given expression

The given expression is ${(5 - \sqrt{10})}^{2} .$

Multiply, using the Product of Binomial Squares Pattern

${(5 - \sqrt{10})}^{2} = 5^{2} - 2 路 5 路 \sqrt{10} - {(\sqrt{10})}^{2}$

02

Part a Step 2. Simplify

By simplifying we get,

$= 5^{2} - 2 路 5 路 \sqrt{10} + {(\sqrt{10})}^{2} = 25 - 10 \sqrt{10} + 10 = 35 - 10 \sqrt{10} [c o m b i n e l i k e t e r m]$

03

Part b Step 1. Multiply the given expression

The given expression is ${(8 + 3 \sqrt{2})}^{2} .$

Multiply, using the Product of Binomial Squares Pattern

${(8 + 3 \sqrt{2})}^{2} = 8^{2} + 2 路 8 路 3 \sqrt{2} + {(3 \sqrt{2})}^{2}$

04

Part b Step 2. Simplify

By simplifying we get,

$= 8^{2} + 2 路 8 路 3 \sqrt{2} + {(3 \sqrt{2})}^{2} = 64 + 48 \sqrt{2} + 18 = 82 + 48 \sqrt{2} [c o m b i n e l i k e t e r m]$

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Most popular questions from this chapter

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

Simplify: $\sqrt{\frac{24 p^{3}}{49}} .$

Write as a radical expression:

(a) $b^{\frac{1}{6}}$

(b) $z^{\frac{1}{5}}$

(c) $p^{\frac{1}{4}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

Explain how you know that

$\sqrt[5]{x^{10}} = x^{2}$

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