# How'd they simplify it to this?

• December 29th 2012, 10:39 AM
Booksrock
How'd they simplify it to this?
In my book, 2(L2+X2)1/2 has been simplified to 2L(1+ X2/L2)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!
• December 29th 2012, 10:51 AM
GJA
Re: How'd they simplify it to this?
Hi Booksrock,

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

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

Technically $(L^{2})^{1/2}=|L|,$ but you said this expression was part of a physics problem, so I'm guessing $L$ 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!
• December 29th 2012, 10:55 AM
Booksrock
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.
• December 29th 2012, 12:34 PM
Deveno
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, A2 = B2 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(L2+X2).

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

4L2(1 + X2/L2) = 4(L2 + L2X2/L2) = 4(L2 + X2).

seems legit.