1. ## Powers and roots

Hello

The problem says to insert brackets to make this a true statement

$
\sqrt{2}^{{\sqrt{2}}^{{\sqrt{2}}^{\sqrt{2}}}} =
\sqrt{2}^{{\sqrt{2}}^{\sqrt{2}}}
$

I know that:

$
\sqrt{2}^{\sqrt{2}} = 2^{\frac{\sqrt2}{2}}
$

$
(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = 2
$

I'm not sure how to proceed from here, apart from brute force. A hint would be appreciated.

2. Hello !

Noting that $(\sqrt{2}^{\sqrt{2}})^{\sqrt{2}} = 2$ is a good thing !

However, and pardon me for that, but I don't know how I got to the answer... It was quite automatic

$\sqrt{2}^{\left(\left({\sqrt{2}}^{\sqrt{2}}\right) ^{\sqrt{2}}\right)}=\left(\sqrt{2}^{\sqrt{2}}\righ t)^{\sqrt{2}}$

(it equals 2)

3. Originally Posted by Moo
However, and pardon me for that, but I don't know how I got to the answer... It was quite automatic
i see, your genius is a mystery--even to you!

4. Dear Moo

Thank you!

Guess I'll just have to work on developing the kind of automatic response you have.

Ting

5. Originally Posted by Jhevon
i see, your genius is a mystery--even to you!
Lol am I able not to agree ?
Originally Posted by Ting
Dear Moo

Thank you!

Guess I'll just have to work on developing the kind of automatic response you have.

Ting
You're welcome !
Actually, I think that at first I was telling myself that the RHS needed parentheses. Making parentheses over the last 2 sqrt(2) wouldn't have made the problem easier. So if there were, it should have been over the first two sqrt(2)

After that...blackout...

6. Originally Posted by Moo
Lol am I able not to agree ?
no

... After that...blackout...
yup, she turned into the super math-solving Hulk.