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

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

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

The square of \sqrt{2} is 2.

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

Multiply 9 and 2 to get 18.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{18}{4}$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$