Q. 217 - Intermediate Algebra

Question

Simplify:

$\frac{2}{3}\sqrt{27}+\frac{3}{4}\sqrt{48}$

Step-by-Step Solution

Answer

The value of the given expression is $5\sqrt{3}.$

Step 1. Given Information

The given expression is

 $\frac{2}{3}\sqrt{27}+\frac{3}{4}\sqrt{48}.$

Step 2. Simplify the radicals

Like radicals can be added or subtracted so,

$$\begin{gathered} \left(\frac{2}{3}·\sqrt{3}·\sqrt{9}\right)+\left(\frac{3}{4}·\sqrt{16}·\sqrt{3}\right) \\ =\left(\frac{2}{3}·\sqrt{3}·3\right)+\left(\frac{3}{4}·4·\sqrt{3}\right) \\ =\left(2\sqrt{3}\right)+\left(3\sqrt{3}\right) \\ =5\sqrt{3} \end{gathered}$$