Solve (frac{sqrt{2}}{sqrt{3}})^2

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

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

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

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

To raise \frac{\sqrt{6}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

The square of \sqrt{6} is 6.

$$\frac{6}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{6}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

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

Factor

$$\frac{2}{3} = 0.6666666666666666$$