is 4 greater than the square root of 32 over 2

Yes, and here's why.

I don't feel like being all complicated so I'm just gonna go with this.

1. Go to the next perfect square up. In this case, it'll be 36
2. Take the root of 36 and put it over 2.
3. 6/2 = 3
4. 4 > 3

\frac{\sqrt{32}}{2}=\frac{\sqrt{16*2}}{2}=\frac{4\sqrt2}{2}=2\sqrt2$$

Since √2 < 2 then 2√2 < 4

Also: nice piece of reasoning by Goldenleaf!

Yes It was good reasoning by GoldenLeaf 

I would like to set it out a little differently though.

$$\frac{\sqrt{32}}{2}<\frac{\sqrt{36}}{2}\\\\ \mbox{therefore}\\\\ \frac{\sqrt{32}}{2}<\frac{6}{2}\\\\ \frac{\sqrt{32}}{2}<3\\\\ and\\\\ \frac{\sqrt{32}}{2}<3<4\\\\ therefore\\\\ \frac{\sqrt{32}}{2}<4\\\\$$

So yes, 4 is not greater than sqrt(32)/2

Excellent logic GoldenLeaf