Solve (frac{12sqrt{5}}{35})^2

$$( \frac { 12 \sqrt { 5 } } { 35 } ) ^ { 2 }$$

Evaluate

$$\frac{144}{245}\approx 0.587755102$$

Solution Steps

To raise \frac{12\sqrt{5}}{35} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(12\sqrt{5}\right)^{2}}{35^{2}}$$

Expand \left(12\sqrt{5}\right)^{2}.

$$\frac{12^{2}\left(\sqrt{5}\right)^{2}}{35^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{144\left(\sqrt{5}\right)^{2}}{35^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{144\times 5}{35^{2}}$$

Multiply 144 and 5 to get 720.

$$\frac{720}{35^{2}}$$

Calculate 35 to the power of 2 and get 1225.

$$\frac{720}{1225}$$

Reduce the fraction \frac{720}{1225} to lowest terms by extracting and canceling out 5.

$$\frac{144}{245}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{5 \cdot 7 ^ {2}} = 0.5877551020408164$$