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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 245 (page 1076)

Evaluate the expression :
$(a) (\sqrt{15 y}) (\sqrt{5 y^{3}}) (b) (\sqrt{2 n^{2}}) (\sqrt{18 n^{3}}) .$ .

Short Answer

Expert verified

$(a) 5 \sqrt{3} y^{2} . (b) 6 n^{\frac{5}{2} .}$

Step by step solution

01

Step 1. Given Information.

The given expression is :

$(a) (\sqrt{15 y}) (\sqrt{5 y^{3}}) (b) (\sqrt{2 n^{2}}) (\sqrt{18 n^{3}}) .$

02

(a) Step 2. Evaluate.

Multiplying the exponents, we get

$= (\sqrt{15 y}) (\sqrt{5 y^{3}}) = \sqrt{15} 脳 \sqrt{5} 脳 \sqrt{y} 脳 y^{\frac{3}{2}} = \sqrt{5 脳 3} 脳 \sqrt{5} 脳 \sqrt{y} 脳 y^{\frac{3}{2}} = \sqrt{3} 脳 5 脳 \sqrt{y} 脳 y^{\frac{3}{2}} = \sqrt{3} 脳 5 脳 \sqrt{y} 脳 y^{\frac{3}{2}} = 5 \sqrt{3} y^{2} .$

03

(b) Step 3. Evaluate.

$= (\sqrt{2 n^{2}}) (\sqrt{18 n^{3}}) = \sqrt{2} 脳 \sqrt{18} 脳 n 脳 n^{\frac{3}{2}} = 3 脳 2 脳 n^{\frac{5}{2}} = 6 n^{\frac{5}{2}} .$

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