Q. 8.82 Simplify:聽(26y4)(1230y)(-49a34)... [FREE SOLUTION]

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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. 8.82 (page 793)

Simplify:
$(2 \sqrt{6 y^{4}}) (12 \sqrt{30 y})$
$(- 4 \sqrt[4]{9 a^{3}}) (3 \sqrt[4]{27 a^{2}})$

Short Answer

Expert verified

Part a. $\begin{array}{rcl} 144 y^{2} \sqrt{5 y} \end{array}$

Part b. $\begin{array}{rcl} - 36 a \sqrt[4]{3 a} \end{array}$

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} 路 \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

$\begin{array}{rcl} (2 \sqrt{6 y^{4}}) (12 \sqrt{30 y}) & = & 2 路 12 路 (\sqrt{6 y^{4}} 路 \sqrt{30 y}) \\ = & 24 \sqrt{6 y^{4} 路 30 y} \\ = & 24 \sqrt{180 y^{5}} \end{array}$

Now, the radical can be simplified as

$\begin{array}{rcl} 24 \sqrt{180 y^{5}} & = & 24 \sqrt{36 y^{4} 路 5 y} \\ = & 24 \sqrt{36 y^{4}} 路 \sqrt{5 y} \\ = & 24 路 6 y^{2} \sqrt{5 y} \\ = & 144 y^{2} \sqrt{5 y} \end{array}$

Part (b) Step 1. Multiply the radicals and simplify

Using the product property of roots that is $\sqrt[n]{a} 路 \sqrt[n]{b} = \sqrt[n]{a b}$ , the expression can be simplified to

$\begin{array}{rcl} (- 4 \sqrt[4]{9 a^{3}}) (3 \sqrt[4]{27 a^{2}}) & = & (- 4) 路 3 路 (\sqrt[4]{9 a^{3}} 路 \sqrt[4]{27 a^{2}}) \\ = & - 12 \sqrt[4]{9 a^{3} 路 27 a^{2}} \\ = & - 12 \sqrt[4]{243 a^{5}} \end{array}$

Now, the radical can be simplified as

$\begin{array}{rcl} - 12 \sqrt[4]{243 a^{5}} & = & - 12 \sqrt[4]{81 a^{4} 路 3 a} \\ = & - 12 \sqrt[4]{81 a^{4}} 路 \sqrt[4]{3 a} \\ = & - 12 路 3 a 路 \sqrt[4]{3 a} \\ = & - 36 a \sqrt[4]{3 a} \end{array}$

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91影视

Simplify:
$(2 \sqrt{6 y^{4}}) (12 \sqrt{30 y})$
$(- 4 \sqrt[4]{9 a^{3}}) (3 \sqrt[4]{27 a^{2}})$

Short Answer

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Part (b) Step 1. Multiply the radicals and simplify

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91影视

Simplify:(26y4)(1230y)(-49a34)(327a24)

Short Answer

Step by step solution

Part (a) Step 1. Multiply the radicals and simplify

Part (b) Step 1. Multiply the radicals and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Simplify:
$(2 \sqrt{6 y^{4}}) (12 \sqrt{30 y})$
$(- 4 \sqrt[4]{9 a^{3}}) (3 \sqrt[4]{27 a^{2}})$