How'd they simplify it to this?

In my book, 2(L^{2}+X^{2})^{1/2} has been simplified to 2L(1+ X^{2}/L^{2})^{1/2. }

I was wondering how exactly have they factorized this? Also, the power of half cannot be removed because later on, I have to apply binomial to this, If someone would explain this to me, it'd be a big,big help. I've spent so much time on this.

This is actually a part of a physics question, and unless I don't get this part, I won't be able to solve it.

This is kinda urgent, I've got a big exam on tuesday, and it includes questions which involve this kind of simplification.

oh and, thank you in advance!

Re: How'd they simplify it to this?

Hi Booksrock,

$\displaystyle 2(L^{2}+X^{2})^{1/2}=2(L[1+X^{2}/L^{2}])^{1/2}=2(L^{2})^{1/2}(1+X^{2}/L^{2})^{1/2} $

$\displaystyle =2L(1+X^{2}/L^{2})^{1/2}$

Technically $\displaystyle (L^{2})^{1/2}=|L|,$ but you said this expression was part of a physics problem, so I'm guessing $\displaystyle L$ is a nonnegative number which is why the there are no absolute value bars in the above equality.

Does this clear things up? Good luck!

Re: How'd they simplify it to this?

THANK YOU THANK YOU THANK YOU!

I did guess this, but I thought it might not be right, because math isn't one of my subjects, and physics without math is pretty killing.

Re: How'd they simplify it to this?

IF...everything in sight is positive, we can check the equality of 2 expressions with square roots by squaring:

if A,B > 0, then if A = B, A^{2} = B^{2} and vice versa (if we don't have positive quantities then the "vice versa" part doesn't work, we might have A = -B).

so...let's square both sides.

on the left (in this corner, the heavyweight champion of the nasty radicals.....) we have:

4(L^{2}+X^{2}).

on the right (and in this corner, our challenger, undefeated in 7 straight head-bangings....) we get:

4L^{2}(1 + X^{2}/L^{2}) = 4(L^{2} + L^{2}X^{2}/L^{2}) = 4(L^{2} + X^{2}).

seems legit.