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

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

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\left(-\frac{\sqrt{10}}{2}\right)^{2}$$

Calculate -\frac{\sqrt{10}}{2} to the power of 2 and get \left(\frac{\sqrt{10}}{2}\right)^{2}.

$$\left(\frac{\sqrt{10}}{2}\right)^{2}$$

To raise \frac{\sqrt{10}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{10}\right)^{2}}{2^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{10}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$