Solve 1-(frac{-2sqrt{3}}{2sqrt{31}})^2

$$1 - ( \frac { - 2 \sqrt { 3 } } { 2 \sqrt { 31 } } ) ^ { 2 }$$

Evaluate

$$\frac{28}{31}\approx 0.903225806$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$1-\left(\frac{-\sqrt{3}}{\sqrt{31}}\right)^{2}$$

Rationalize the denominator of \frac{-\sqrt{3}}{\sqrt{31}} by multiplying numerator and denominator by \sqrt{31}.

$$1-\left(\frac{-\sqrt{3}\sqrt{31}}{\left(\sqrt{31}\right)^{2}}\right)^{2}$$

The square of \sqrt{31} is 31.

$$1-\left(\frac{-\sqrt{3}\sqrt{31}}{31}\right)^{2}$$

To multiply \sqrt{3} and \sqrt{31}, multiply the numbers under the square root.

$$1-\left(\frac{-\sqrt{93}}{31}\right)^{2}$$

To raise \frac{-\sqrt{93}}{31} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(-\sqrt{93}\right)^{2}}{31^{2}}$$

Expand \left(-\sqrt{93}\right)^{2}.

$$1-\frac{\left(-1\right)^{2}\left(\sqrt{93}\right)^{2}}{31^{2}}$$

Calculate -1 to the power of 2 and get 1.

$$1-\frac{1\left(\sqrt{93}\right)^{2}}{31^{2}}$$

The square of \sqrt{93} is 93.

$$1-\frac{1\times 93}{31^{2}}$$

Multiply 1 and 93 to get 93.

$$1-\frac{93}{31^{2}}$$

Calculate 31 to the power of 2 and get 961.

$$1-\frac{93}{961}$$

Reduce the fraction \frac{93}{961} to lowest terms by extracting and canceling out 31.

$$1-\frac{3}{31}$$

Subtract \frac{3}{31} from 1 to get \frac{28}{31}.

$$\frac{28}{31}$$

Factor

$$\frac{2 ^ {2} \cdot 7}{31} = 0.9032258064516129$$