Q. 589 - Intermediate Algebra

Question

In the following exercises, simplify. Assume all variables are positive.

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

Step-by-Step Solution

Answer

The simplified expression is $36x^4.$

Step 1. Given information

We have

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

Step 2. Factor the radicand with power of index

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

Step 3. Simplify the root of the power

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