# Easy question about the root (of a real number)

1. Oct 23, 2009

### joris_pixie

[SOLVED] Easy question about the root (of a real number)

Hi, i'm a bit embarresed to ask this but does anybody know how to get this:
$$\sqrt{3 - 2\sqrt{2}} = \sqrt{2} - 1$$

?

Last edited: Oct 23, 2009
2. Oct 23, 2009

### S_David

$$\sqrt{3 - 2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}$$

what is the relationship between $$\left(2-2\sqrt{2}+1\right)$$ and $$\left(\sqrt{2} - 1\right)$$??

3. Oct 23, 2009

### phyzmatix

I must say that this one does require a bit of clever thinking. I can add that the best way to "see" the answer is to take your equation

$$\sqrt{3-2\sqrt{2}}=\sqrt{2}-1$$

and solve it as is (this will ultimately lead you to what S_David is pointing out).

4. Oct 23, 2009

### joris_pixie

OK! Got it !
Sorry for wasting your time and thank you !! :)

It's true that it is one you have to 'see' !
And if you 'see it' it's easy, but if you don't ...

But thanks a lot you guys, got it now!

Last edited: Oct 23, 2009
5. Oct 23, 2009

### phyzmatix

Definitely didn't waste my time. You forced me to think, which is always good!