Chapter 8: Q. 589 (page 857)

In the following exercises, simplify. Assume all variables are positive.
$2 \sqrt{12 x^{5}} . 3 \sqrt{6 x^{3}}$

Short Answer

Expert verified

The simplified expression is $36 x^{4} .$

Step by step solution

Step 1. Given information

We have

2 \sqrt{12 x^{5}} . 3 \sqrt{6 x^{3}}

Step 2. Factor the radicand with power of index

$= 2 \sqrt{12 x^{5}} \times 3 \sqrt{6 x^{3}} = 2 \times 3 \sqrt{2^{2} \times 3 \times x^{2} \times x^{2} \times x} \times \sqrt{6 \times x^{2} \times x} = 6 \times 2 \times x \times x \sqrt{3 x} \times x \sqrt{6 x}$

Step 3. Simplify the root of the power

$= 6 \times 2 \times x \times x \sqrt{3 x} \times x \sqrt{6 x} = 12 x^{3} \sqrt{18 x^{2}} = 12 x^{3} \sqrt{3^{2} x^{2}} = 12 x^{3} \times x \times 3 = 36 x^{4}$

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In the following exercises, simplify. Assume all variables are positive.
$2 \sqrt{12 x^{5}} . 3 \sqrt{6 x^{3}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor the radicand with power of index

Step 3. Simplify the root of the power

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In the following exercises, simplify. Assume all variables are positive.212x5.36x3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factor the radicand with power of index

Step 3. Simplify the root of the power

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Calculus

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify. Assume all variables are positive.
$2 \sqrt{12 x^{5}} . 3 \sqrt{6 x^{3}}$