Solve (frac{15sqrt{3}}{4})^2

$$( \frac { 15 \sqrt { 3 } } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{675}{16}=42.1875$$

Solution Steps

To raise \frac{15\sqrt{3}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(15\sqrt{3}\right)^{2}}{4^{2}}$$

Expand \left(15\sqrt{3}\right)^{2}.

$$\frac{15^{2}\left(\sqrt{3}\right)^{2}}{4^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{225\left(\sqrt{3}\right)^{2}}{4^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{225\times 3}{4^{2}}$$

Multiply 225 and 3 to get 675.

$$\frac{675}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{675}{16}$$

Factor

$$\frac{3 ^ {3} \cdot 5 ^ {2}}{2 ^ {4}} = 42\frac{3}{16} = 42.1875$$