Solve (-sqrt{5/3})^2=

$$( - \sqrt { \frac { 5 } { 3 } } ) ^ { 2 } =$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\left(-\frac{\sqrt{5}}{\sqrt{3}}\right)^{2}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\left(-\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}$$

The square of \sqrt{3} is 3.

$$\left(-\frac{\sqrt{5}\sqrt{3}}{3}\right)^{2}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\left(-\frac{\sqrt{15}}{3}\right)^{2}$$

Calculate -\frac{\sqrt{15}}{3} to the power of 2 and get \left(\frac{\sqrt{15}}{3}\right)^{2}.

$$\left(\frac{\sqrt{15}}{3}\right)^{2}$$

To raise \frac{\sqrt{15}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{15}\right)^{2}}{3^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{15}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{15}{9}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$