Chapter 8.1, Problem 14CE

To determine

To Simplify: Simplify the given expression

Answer to Problem 14CE

The simplified form is $\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{2}\sqrt{\frac{7}{3}}$

Explanation of Solution

Given information: The given expression is $\frac{3}{4}\sqrt{\frac{28}{3}}$

We have the given expression is $\frac{3}{4}\sqrt{\frac{28}{3}}$

It can be further written as

  $\begin{array}{c}\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{4}\sqrt{\frac{2^2\times 7}{3}}\\ =\frac{3}{4}\times 2\sqrt{\frac{7}{3}}\\ =\frac{3}{2}\sqrt{\frac{7}{3}}\end{array}$

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is $\frac{3}{4}\sqrt{\frac{28}{3}}=\frac{3}{2}\sqrt{\frac{7}{3}}$