Understanding an Equation: $\frac {1}{2\sqrt{2}} = \frac{\sqrt2} {4}$

[tmt1]

On the board, the professor made a note that:

$$\frac {1}{2\sqrt{2}}$$ is equal to

$$\frac{\sqrt2} {4}$$

I don't see how this is. Can someone explain this? I've tried to work it out a few ways.

 

[mathbalarka]

Note that

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

 

[MarkFL]

He rationalized the denominator:

$$\frac{1}{2\sqrt{2}}=\frac{1}{2\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{4}$$