Solve {left(5/2sqrt{5}right)}^2

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

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

Cancel out 5 in both numerator and denominator.

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

To raise \frac{\sqrt{5}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

The square of \sqrt{5} is 5.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$