Solve (7)^2-(frac{5sqrt{3}}{2})^2

$$( 7 ) ^ { 2 } - ( \frac { 5 \sqrt { 3 } } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{121}{4}=30.25$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49-\left(\frac{5\sqrt{3}}{2}\right)^{2}$$

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

$$49-\frac{\left(5\sqrt{3}\right)^{2}}{2^{2}}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$49-\frac{5^{2}\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$49-\frac{25\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$49-\frac{25\times 3}{2^{2}}$$

Multiply 25 and 3 to get 75.

$$49-\frac{75}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$49-\frac{75}{4}$$

Subtract \frac{75}{4} from 49 to get \frac{121}{4}.

$$\frac{121}{4}$$

Factor

$$\frac{11 ^ {2}}{2 ^ {2}} = 30\frac{1}{4} = 30.25$$