Solve (-3sqrt{2/3})^2

$$( - 3 \sqrt { \frac { 2 } { 3 } } ) ^ { 2 }$$

Evaluate

$$6$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

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

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Cancel out 3 and 3.

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

Expand \left(-\sqrt{6}\right)^{2}.

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

Calculate -1 to the power of 2 and get 1.

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

The square of \sqrt{6} is 6.

$$1\times 6$$

Multiply 1 and 6 to get 6.

$$6$$

Factor

$$2\times 3$$