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

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Calculate -\frac{\sqrt{3}}{3} to the power of 2 and get \left(\frac{\sqrt{3}}{3}\right)^{2}.

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

To raise \frac{\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

The square of \sqrt{3} is 3.

$$\frac{3}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$