Solve (5sqrt{5})^2+(2/5)^3

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

Evaluate

$$\frac{15633}{125}=125.064$$

Solution Steps

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

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

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{5}\right)^{2}+\left(\frac{2}{5}\right)^{3}$$

The square of \sqrt{5} is 5.

$$25\times 5+\left(\frac{2}{5}\right)^{3}$$

Multiply 25 and 5 to get 125.

$$125+\left(\frac{2}{5}\right)^{3}$$

Calculate \frac{2}{5} to the power of 3 and get \frac{8}{125}.

$$125+\frac{8}{125}$$

Add 125 and \frac{8}{125} to get \frac{15633}{125}.

$$\frac{15633}{125}$$

Factor

$$\frac{3 ^ {4} \cdot 193}{5 ^ {3}} = 125\frac{8}{125} = 125.064$$