Hi Booksrock,
Technically but you said this expression was part of a physics problem, so I'm guessing 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!
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!
Hi Booksrock,
Technically but you said this expression was part of a physics problem, so I'm guessing 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!
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.