Solve (frac{3sqrt{2}}{5})^2

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

Evaluate

$$\frac{18}{25}=0.72$$

Solution Steps

To raise \frac{3\sqrt{2}}{5} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(3\sqrt{2}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9\left(\sqrt{2}\right)^{2}}{5^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{9\times 2}{5^{2}}$$

Multiply 9 and 2 to get 18.

$$\frac{18}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{18}{25}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{5 ^ {2}} = 0.72$$