Solve 2-(2/sqrt{6})^2

$$2 - ( \frac { 2 } { \sqrt { 6 } } ) ^ { 2 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Rationalize the denominator of \frac{2}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Divide 2\sqrt{6} by 6 to get \frac{1}{3}\sqrt{6}.

$$2-\left(\frac{1}{3}\sqrt{6}\right)^{2}$$

Expand \left(\frac{1}{3}\sqrt{6}\right)^{2}.

$$2-\left(\frac{1}{3}\right)^{2}\left(\sqrt{6}\right)^{2}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$2-\frac{1}{9}\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$2-\frac{1}{9}\times 6$$

Multiply \frac{1}{9} and 6 to get \frac{2}{3}.

$$2-\frac{2}{3}$$

Subtract \frac{2}{3} from 2 to get \frac{4}{3}.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$