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

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

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

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

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

Express 3\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

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

The square of \sqrt{3} is 3.

$$\frac{3\times 3}{2^{2}}$$

Multiply 3 and 3 to get 9.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$