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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. 206 (page 798)

In the following exercises, multiply:
$(a) {(4 + \sqrt{11})}^{2} (b) {(3 - 2 \sqrt{5})}^{2}$

Short Answer

Expert verified

Part a. By multiplying we get, $27 + 8 \sqrt{11} .$

Part b. By multiplying we get, $29 - 12 \sqrt{5} .$

Step by step solution

01

Part (a) Step 1. Multiply the given expression

The given expression is ${(4 + \sqrt{11})}^{2}$

Multiply, using the Product of Binomial Squares Pattern

${(4 + \sqrt{11})}^{2} = 4^{2} + 2 路 4 路 \sqrt{11} + {(\sqrt{11})}^{2}$

02

Part (a) Step 2. Simplify

By simplifying we get,

$= 4^{2} + 2 路 4 路 \sqrt{11} + {(\sqrt{11})}^{2} = 16 + 8 \sqrt{11} + 11 = 27 + 8 \sqrt{11} [c o m b i n e l i k e t e r m s]$

03

Part (b) Step 1. Multiply the given expression

The given expression is ${(3 - 2 \sqrt{5})}^{2} .$

Multiply, using the Product of Binomial Squares Pattern

${(3 - 2 \sqrt{5})}^{2} = 3^{2} - 2 路 3 路 2 \sqrt{5} + {(2 \sqrt{5})}^{2}$

04

Part (b) Step 2. Simplify

By simplifying we get,

$= 3^{2} - 2 路 3 路 2 \sqrt{5} + {(2 \sqrt{5})}^{2} = 9 - 12 \sqrt{5} + 20 = 29 - 12 \sqrt{5}$

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Simplify:

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