Solve (sqrt{2}-1/sqrt{2})^2=?

$$( \sqrt { 2 } - \frac { 1 } { \sqrt { 2 } } ) ^ { 2 } = ?$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Combine \sqrt{2} and -\frac{\sqrt{2}}{2} to get \frac{1}{2}\sqrt{2}.

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

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

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

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{1}{4}\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$\frac{1}{4}\times 2$$

Multiply \frac{1}{4} and 2 to get \frac{1}{2}.

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

Factor

$$\frac{1}{2} = 0.5$$