Chapter 12.4, Problem 2MRE

To determine

To simplify: the given expression.

Answer to Problem 2MRE

The simplified form of the expression is $\frac{3c^4}{5}$ .

Explanation of Solution

Given information:

Given expression,

  $\sqrt{\frac{12c^3}{5}}\cdot \sqrt{\frac{3c^5}{20}}$

Calculation:

Consider the given expression:

  $\sqrt{\frac{12c^3}{5}}\cdot \sqrt{\frac{3c^5}{20}}$

Now, simplify the expression as shown,

  $\begin{array}{c}\sqrt{\frac{12c^3}{5}}\cdot \sqrt{\frac{3c^5}{20}}=\sqrt{\frac{12c^3}{5}\cdot \frac{3c^5}{20}}\\ =\frac{\sqrt{36c^{5+3}}}{\sqrt{5\cdot 20}}\\ =\frac{\sqrt{36c^8}}{\sqrt{100}}\\ =\frac{\sqrt{6c^4\times 6c^4}}{\sqrt{10\times 10}}\\ =\frac{6c^4}{10}\\ =\frac{3c^4}{5}\end{array}$

Hence, the simplified form of the expressionis $\frac{3c^4}{5}$ .