Question

Simplify each expression.

${\left(\frac{2}{3}\sqrt{6}\right)}^2$

Short answer

The simplified form is,

${\left(\frac{2}{3}\sqrt{6}\right)}^2=\frac{8}{3}$.

Step-by-step solution

Step 1. Given information.

The given expression is,

${\left(\frac{2}{3}\sqrt{6}\right)}^2$.

Step 2. It can be further written as below.

We have the given expression is ${\left(\frac{2}{3}\sqrt{6}\right)}^2$

Then,

$\begin{array}{c}{\left(\frac{2}{3}\sqrt{6}\right)}^2=\left(\frac{2}{3}\sqrt{6}\right)\left(\frac{2}{3}\sqrt{6}\right)\\ =\left(\frac{2^2}{3^2}\sqrt{6}.\sqrt{6}\right)\\ =\left(\frac{4}{9}\sqrt{6^2}\right)\\ =\frac{4}{9}\times 6\\ =\frac{4}{3}\times 2\\ =\frac{8}{3}\end{array}$

Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

Therefore, the simplified form is, ${\left(\frac{2}{3}\sqrt{6}\right)}^2=\frac{8}{3}$.