Solve sqrt{2-(frac{sqrt{6}}{2})^2}

$$\sqrt { 2 - ( \frac { \sqrt { 6 } } { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

To raise \frac{\sqrt{6}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\sqrt{2-\frac{\left(\sqrt{6}\right)^{2}}{2^{2}}}$$

The square of \sqrt{6} is 6.

$$\sqrt{2-\frac{6}{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{2-\frac{6}{4}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{2-\frac{3}{2}}$$

Subtract \frac{3}{2} from 2 to get \frac{1}{2}.

$$\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}$$