Solve {left(1102/2sqrt{frac{5{}}}right)}^2

$${ \left(1 \frac{ 102 }{ 2 \sqrt{ \frac{ 5 }{ } } } \right) }^{ 2 }$$

Evaluate

$$\frac{2601}{5}=520.2$$

Solution Steps

Anything divided by one gives itself.

$$\left(1\times \frac{102}{2\sqrt{5}}\right)^{2}$$

Rationalize the denominator of \frac{102}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\left(1\times \frac{102\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}\right)^{2}$$

The square of \sqrt{5} is 5.

$$\left(1\times \frac{102\sqrt{5}}{2\times 5}\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$\left(1\times \frac{51\sqrt{5}}{5}\right)^{2}$$

Express 1\times \frac{51\sqrt{5}}{5} as a single fraction.

$$\left(\frac{51\sqrt{5}}{5}\right)^{2}$$

To raise \frac{51\sqrt{5}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(51\sqrt{5}\right)^{2}}{5^{2}}$$

Expand \left(51\sqrt{5}\right)^{2}.

$$\frac{51^{2}\left(\sqrt{5}\right)^{2}}{5^{2}}$$

Calculate 51 to the power of 2 and get 2601.

$$\frac{2601\left(\sqrt{5}\right)^{2}}{5^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{2601\times 5}{5^{2}}$$

Multiply 2601 and 5 to get 13005.

$$\frac{13005}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{13005}{25}$$

Reduce the fraction \frac{13005}{25} to lowest terms by extracting and canceling out 5.

$$\frac{2601}{5}$$

Factor

$$\frac{3 ^ {2} \cdot 17 ^ {2}}{5} = 520\frac{1}{5} = 520.2$$