Q. 225 - Intermediate Algebra

Question

1Simplify:

$\frac{3}{5}\sqrt{75}-\frac{1}{4}\sqrt{48}$

Step-by-Step Solution

Answer

The value of the given expression is $2\sqrt{3}$

Step 1. Given information

The given expression is $\frac{3}{5}\sqrt{75}-\frac{1}{4}\sqrt{48}$

Step 2. simplifying the radicals

Simplifying the radicals, we get:

$$\begin{gathered} \frac{3}{5}\sqrt{75}-\frac{1}{4}\sqrt{48} \\ \frac{3}{5}\sqrt{25·3}-\frac{1}{4}\sqrt{16·3} \\ \frac{3}{5}·5\sqrt{3}-\frac{1}{4}·4\sqrt{3} \left[\sqrt{25}=5,\sqrt{16}=4\right] \\ 3\sqrt{3}-\sqrt{3} \end{gathered}$$

Subtracting the like radicals, we get:

$$\begin{gathered} 3\sqrt{3}-\sqrt{3} \\ 2\sqrt{3} \end{gathered}$$