Question

Im drawing a blank on this?... why is 1/sqrt2/2 equal to sqrt 2? I thought it rationalized to 1?

Answer 1

It's hard to read your crazy totem pole there.
\[\large\rm \frac{1}{\left(\frac{\sqrt2}{2}\right)}\]Is this what we're dealing with?

Answer 2

yes. :)

Answer 3

Recall:\[\large\rm \frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}=\frac{a}{b}\cdot\frac{d}{c}\]Maybe you've learned it as "Keep Change Flip" or something similar.

Answer 4

So for your problem:\[\large\rm \frac{1}{\left(\frac{\sqrt2}{2}\right)}=1\cdot\frac{2}{\sqrt2}\]

Answer 5

And from there, sure you can rationalize,\[\large\rm \frac{2}{\sqrt2}\cdot\color{royalblue}{\frac{\sqrt2}{\sqrt2}}=\frac{2\sqrt2}{2}\]

Answer 6

Great!..... ok . I see what I was doing. I was just flipping it and multiplying. Thank you

Answer 7

c: