how to put an expression under the square root?

Jun 2010
13
0
So, let's say that you have this expression:
(x - a)

and you need to get it under the square root sign. What is the right way to do it?

I came up with two methods, hopefully at least one of them is right. I want to find out which is right and to read more on the topic in order to understand WHY it is right.

First way:


\(\displaystyle
x - a = \sqrt{x^2 - a^2} = \sqrt{(x-a)(x+a)}

\)



Second way:


\(\displaystyle
x - a = \sqrt{(x-a)^2} = \sqrt{x^2 - 2xa + a^2}

\)



I can't find any videos on youtube or texts on the math sites, because I don't know which keywords to use in order to find it - any help would be appreciated.
 

mr fantastic

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So, let's say that you have this expression:
(x - a)

and you need to get it under the square root sign. What is the right way to do it?

I came up with two methods, hopefully at least one of them is right. I want to find out which is right and to read more on the topic in order to understand WHY it is right.

First way:


\(\displaystyle x - a = \sqrt{x^2 - a^2} = \sqrt{(x-a)(x+a)}\) Mr F says: This is totally wrong. What happens if x = 2 and a = 1, for example? You're meant to learn something from previous questions that you posted: http://www.mathhelpforum.com/math-help/pre-algebra-algebra/148619-square-root-1-equal-1-a.html

Second way:

\(\displaystyle x - a = \sqrt{(x-a)^2} = \sqrt{x^2 - 2xa + a^2}\) Mr F says: This is wrong too. \(\displaystyle \sqrt{(x - a)^2} = |x - a|\) not x - a.

I can't find any videos on youtube or texts on the math sites, because I don't know which keywords to use in order to find it - any help would be appreciated.
Perhaps you should post the real question (the one that has led to what you posted).