Solve (-3sqrt{1/3})^2

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

Evaluate

$$3$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

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

Expand \left(-\sqrt{3}\right)^{2}.

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

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

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

The square of \sqrt{3} is 3.

$$1\times 3$$

Multiply 1 and 3 to get 3.

$$3$$

Factor

$$3$$