How $\frac{1}{\sqrt{2}}$ can be equal to $\frac{\sqrt{2}}{2}$? How $\frac{1}{\sqrt{2}}$ can be equal to $\frac{\sqrt{2}}{2}$?
I got answer $\frac{1}{\sqrt{2}}$, but the real answer is $\frac{\sqrt{2}}{2}$. Anyway, calculator for both answers return same numbers.

Let's square both of them:
\begin{align}
\sqrt{\frac{1}{2}}^2 &= \frac{1}{2}, \text{ while} \\
\left(\frac{\sqrt{2}}{2}\right)^2 
&=\frac{\sqrt{2}^2}{2^2} \\ 
&=\frac{2}{4} \\
&= \frac{1}{2} 
\end{align}
So they're both positive numbers, and their squares are the same, so they must be the same. 
