Chapter 11.8, Problem 27WE

To determine

To find: The simplification of the given expression.

Answer to Problem 27WE

The simplification of the given expression is $-\frac{\sqrt{3}}{3}$ .

Explanation of Solution

Given information:

The given expression is,

  $3\sqrt{3}-2\sqrt{12}+4\sqrt{\frac{1}{3}}$

The given expression is simplified as,

  $\begin{array}{c}3\sqrt{3}-2\sqrt{12}+4\sqrt{\frac{1}{3}}=3\sqrt{3}-2\sqrt{12}+4\frac{\sqrt{1}}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}\\ =3\sqrt{3}-2\sqrt{4\times 3}+4\frac{\sqrt{3}}{3}\\ =\sqrt{3}\left(3-4+\frac{4}{3}\right)\\ =-\frac{\sqrt{3}}{3}\end{array}$

Thus, the simplification of the given expression is $-\frac{\sqrt{3}}{3}$ .