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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.521 (page 853)

In the following exercise simplify
$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

Short Answer

Expert verified

Simplifying,

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}} = 37 \sqrt{3} y$

Step by step solution

01

Step 1. Given information

We have given,

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

02

Step 2. Concept

Here we can factor the numbers and then we will use radical rule,

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

Also,

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

03

Step 3. Explanation

We have,

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

Simplifying it,

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}} = 3 \sqrt{25 脳 3 y^{2}} + 8 y \sqrt{16 脳 3} - \sqrt{100 脳 3 y^{2}}$

Using radical rule,

$3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}} = 3 路鈥� 5 \sqrt{3} \sqrt{y^{2}} + 8 y 路鈥� 4 \sqrt{3} - 10 \sqrt{3} y$

$鈬� 3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}} = 15 y \sqrt{3} + 32 y \sqrt{3} - 10 y \sqrt{3} = (15 + 32 - 10) y \sqrt{3} = 37 \sqrt{3} y$

04

Step 4. Conclusion

Hence, value of $3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$ is $37 \sqrt{3} y$ .

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Most popular questions from this chapter

In the following exercises, write with a rational exponent.

$\sqrt[3]{7 c} 鈸� \sqrt[7]{12 d} 鈸� 2 \sqrt[4]{6 b}$

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In the following exercises, use the Product Property to simplify radical expression $\sqrt{125} .$

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