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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. 191 (page 798)

In the following exercises, multiply.
a. $\sqrt{7} (5 + 2 \sqrt{7})$
b. $\sqrt[3]{6} (4 + \sqrt[3]{18})$

Short Answer

Expert verified

On multiplication, we get $14 + 5 \sqrt{7}, 4 \sqrt[3]{6} + 3 \sqrt[3]{4}$ respectively

Step by step solution

01

Part (a) Step 1: Given information

Given the expression $\sqrt{7} (5 + 2 \sqrt{7}), \sqrt[3]{6} (4 + \sqrt[3]{18})$

02

Part (a) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$\sqrt{7} (5 + 2 \sqrt{7}) = 5 \sqrt{7} + 2 脳 7 \sqrt{7} (5 + 2 \sqrt{7}) = 5 \sqrt{7} + 14$

03

Part (b) Step 1: Given information

Given expression $\sqrt[3]{6} (4 + \sqrt[3]{18})$

04

Part (b) Step 2: Multiplying the terms and simplifying

Multiplying the terms and simplifying, we get

$\sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 路 \sqrt[3]{6} + \sqrt[3]{6} 路 \sqrt[3]{18} \sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 \sqrt[3]{6} + \sqrt[3]{108} \sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 \sqrt[3]{6} + \sqrt[3]{27.4} \sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 \sqrt[3]{6} + \sqrt[3]{27} 路 \sqrt[3]{4} \sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 \sqrt[3]{6} + \sqrt[3]{(3)^{3}} 路 \sqrt[3]{4} \sqrt[3]{6} (4 + \sqrt[3]{18}) = 4 \sqrt[3]{6} + 3 \sqrt[3]{4}$

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