Solve (1,8sqrt{3})^2-(frac{1sqrt{7}}{2})^2

$$( 1,8 \sqrt { 3 } ) ^ { 2 } - ( \frac { 1 \sqrt { 7 } } { 2 } ) ^ { 2 }$$

Evaluate

$$7,97$$

Solution Steps

Expand \left(1,8\sqrt{3}\right)^{2}.

$$1,8^{2}\left(\sqrt{3}\right)^{2}-\left(\frac{1\sqrt{7}}{2}\right)^{2}$$

Calculate 1,8 to the power of 2 and get 3,24.

$$3,24\left(\sqrt{3}\right)^{2}-\left(\frac{1\sqrt{7}}{2}\right)^{2}$$

The square of \sqrt{3} is 3.

$$3,24\times 3-\left(\frac{1\sqrt{7}}{2}\right)^{2}$$

Multiply 3,24 and 3 to get 9,72.

$$9,72-\left(\frac{1\sqrt{7}}{2}\right)^{2}$$

To raise \frac{1\sqrt{7}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$9,72-\frac{\left(1\sqrt{7}\right)^{2}}{2^{2}}$$

Expand \left(1\sqrt{7}\right)^{2}.

$$9,72-\frac{1^{2}\left(\sqrt{7}\right)^{2}}{2^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$9,72-\frac{1\left(\sqrt{7}\right)^{2}}{2^{2}}$$

The square of \sqrt{7} is 7.

$$9,72-\frac{1\times 7}{2^{2}}$$

Multiply 1 and 7 to get 7.

$$9,72-\frac{7}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$9,72-\frac{7}{4}$$

Subtract \frac{7}{4} from 9,72 to get \frac{797}{100}.

$$\frac{797}{100}$$

Factor

$$\frac{797}{2 ^ {2} \cdot 5 ^ {2}} = 7\frac{97}{100} = 7.97$$