Chapter 6.3, Problem 12OE

To determine

Simplify the expression $\sqrt{\frac{3}{4}}+\sqrt{\frac{27}{4}}$ . If no simplification is possible say so.

Answer to Problem 12OE

The simplified value is $2\sqrt{3}$ .

Explanation of Solution

Given information: The given expression is,

  $\sqrt{\frac{3}{4}}+\sqrt{\frac{27}{4}}\mathrm{......}\left(1\right)$

Calculation: Simplify (1),

  $\begin{array}{c}\sqrt{\frac{3}{4}}+\sqrt{\frac{27}{4}}=\frac{\sqrt{3}}{\sqrt{4}}+\frac{\sqrt{27}}{\sqrt{4}}\mathrm{......}\left\{\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\right\}\\ =\frac{\sqrt{3}}{2}+\frac{\sqrt{\left(9\right)\left(3\right)}}{2}\\ =\frac{\sqrt{3}}{2}+\frac{3\sqrt{3}}{2}\\ =\frac{4\sqrt{3}}{2}\mathrm{......}\left\{\text{Simplified}\right\}\\ =2\sqrt{3}\end{array}$