Q. 223 - Intermediate Algebra

Question

Simplify:

$5\sqrt{12c^4}-3\sqrt{27c^6}$

Step-by-Step Solution

Answer

The value of the given expression is:

$10c^2\sqrt{3}-9c^3\sqrt{3}$

Step 1. Given information

The given expression is: 

$5\sqrt{12c^4}-3\sqrt{27c^6}$

Step 2. Simplifying the radicals

Simplifying the radicals, we get:

$$\begin{gathered} 5\sqrt{12c^4}-3\sqrt{27c^6} \\ 5\sqrt{4c^4·3}-3\sqrt{9c^6·3} \\ 5·2c^2\sqrt{3}-3·3c^3\sqrt{3} [\sqrt{4c^4}=2c^2, \sqrt{9c^6}=3c^3] \\ 10c^2\sqrt{3}-9c^3\sqrt{3} \end{gathered}$$