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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.526 (page 853)

In the following exercises, multiply
$(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11})$

Short Answer

Expert verified

Simplifying, $(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11}) = - 439 - 2 \sqrt{77}$

Step by step solution

01

Step 1. Given information

We have given,

$(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11})$

02

Step 2. Concept

Here we will going to use FOIL method,

$(a + b) (c + d) = a c + a d + b c + b d$

and radical rules,

$\sqrt[n]{a^{n}} = a$

$\sqrt[n]{a} \sqrt[n]{b} = \sqrt[n]{a b}$

03

Step 1. Explanation

We have,

$(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11})$

Using FOIL method,

$2 \sqrt{7} 路鈥� 4 \sqrt{7} + 2 \sqrt{7} 路鈥� 9 \sqrt{11} - 5 \sqrt{11} 路鈥� 4 \sqrt{7} - 5 \sqrt{11} 路鈥� 9 \sqrt{11}$

Using product rule,

$56 + 18 \sqrt{77} - 20 \sqrt{77} - 495$

$鈬� - 439 - 2 \sqrt{77}$

04

Step 4. Conclusion

Hence, multiplying $(2 \sqrt{7} - 5 \sqrt{11}) (4 \sqrt{7} + 9 \sqrt{11})$ we will get, $- 439 - 2 \sqrt{77}$ .

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{450}$

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

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