Solve 7-(frac{3sqrt{7}}{4})^2

$$7 - ( \frac { 3 \sqrt { 7 } } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{49}{16}=3.0625$$

Solution Steps

To raise \frac{3\sqrt{7}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$7-\frac{\left(3\sqrt{7}\right)^{2}}{4^{2}}$$

Expand \left(3\sqrt{7}\right)^{2}.

$$7-\frac{3^{2}\left(\sqrt{7}\right)^{2}}{4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$7-\frac{9\left(\sqrt{7}\right)^{2}}{4^{2}}$$

The square of \sqrt{7} is 7.

$$7-\frac{9\times 7}{4^{2}}$$

Multiply 9 and 7 to get 63.

$$7-\frac{63}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$7-\frac{63}{16}$$

Subtract \frac{63}{16} from 7 to get \frac{49}{16}.

$$\frac{49}{16}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {4}} = 3\frac{1}{16} = 3.0625$$