(√2+√3) - (√2-√3)

You forgot to cut and paste your work and answer like the site rules require.

my attempt:
(√2+√3) - (√2-√3)
=(√2+√3)^2 - (√2-√3)^2
=2+√3-2-√3
=2√3

Very interesting - every line of your work is incorrect, and yet you stumbled into the correct answer!

Starting with:

(\sqrt 2 + \sqrt 3) - (\sqrt 2 - \sqrt 3)

Eliminate the parentheses, being careful to watch signs:

\sqrt 2 + \sqrt 3 - \sqrt 2 + \sqrt 3 = 2 \sqrt 3

So like I said, you ended up with the correct answer. Now here's why your approach is all wrong:

1. First, (\sqrt 2 + \sqrt 3) - (\sqrt 2 - \sqrt 3) does not equal (\sqrt 2 + \sqrt 3)^2 - (\sqrt 2 - \sqrt 3)^2. This is like saying that a +b = a^2 + b^2.

2. Next, (\sqrt 2 + \sqrt 3)^2 - (\sqrt 2 - \sqrt 3)^2 = (\sqrt 2 )^2 + 2 \sqrt 2 \sqrt 3 + (\sqrt 3)^2 - [(\sqrt 2)^2 - 2 \sqrt2 \sqrt 3 + (\sqrt 3 )^2] = 2 + 2 \sqrt2 \sqrt 3 + 3 - (2 - 2 \sqrt 2 \sqrt 3 + 3) = 4 \sqrt 2 \sqrt 3

3. Your third line is equivalent to zero: it's equivalent to a + b - a - b = 0

So I have no idea how you got the correct final answer, unless perhaps you copied it from an answer key?

Post back if you have additional questions about this.