Recent content by chambershex

Thank-you. I now understand why the first question I posed is true, however I'm still yet to really see a good, fundamental explanation of why the second question is true (the one referring to the roots). The overarching reason I am asking these questions is because I have always had a...

I know your being nasty here, but I can answer that. The operation + is fundamental and cannot be broken down into anything more simple - what it means is self-evident. The operation x is derived from +, being defined as Y lots of X. Or alternatively X + X + X..., Y times. However, I'm sure...

That sounds very interesting, and no doubt very complicated ;)

Does the 'dick' in 'dickfore' happen to be a self-description by any chance? And btw finding a question extremely easy does not mean I boast the same intellect as you. So please, calling something 'trolling' because you simply find it trivial is really the height of arrogance. EDIT: I am also...

Haha I should feel bad for starting it? What is this a prestigious science journal? You should should feel bad for showing such pretentiousness. No one had to respond to this thread, but they chose to (including yourself). I already said before I got everything I wanted out this threa, so as far...

Yes of course its enough to prove their different, but it doesn't explain WHY in the same sense that the original question I asked was described (with reference to the distributive law etc.). Also I wonder if its possible to represent the question geometrically much like the first one? But I...

Yeh I intially thought that but realized that was wrong. "It's just going to be some modified version of what I gave" - I thought that too, but I have absolutely no idea how one would derive the answer from that. I suspect it would get quite complicated (but I could easily be wrong), but...

haha, unfortunately that doesn't shine much light on the situation ;)

Hmmm... so there's no way to actually find the difference between the left and right sides of the following equation in terms of the variables a,b? √(a + b) =/= √a + √b It seems you can only find a difference by first getting rid of the root signs by squaring both sides (like Mentallic...

Oh right, I get where you coming from now... So yeh substitution results in: a + b =/= a + 2√(ab) + b Therefore the difference being 2√(ab).

Thanks for the detailed response. So using the same kind of process how can one prove that √(a + b) =/= √a + √b? For the first problem I posed, (x+y)^2 =/= x^2 + y^2, I now understand (thanks to others) why it is so. For the left hand side, the expression (x+y)^2 is equivalent to (x+y)(x+y)...

Sorry I'm not really following your reasoning here. With the first problem I posed, you showed me how the left hand side (x+y)2 can be shown to be an application of the distributive law. However, even if the left hand side of this problem √(a + b) can be framed as (a+b)1/2, it isn't possible to...

And also, just one more question: If the first question I posed can be shown to be true by reducing the binomial square down to an application of the distributive law, what can the following be reduced down to: √(a + b) =/= √a + √b So its pretty much the same question but instead of...

Thanks everyone for the input. I was thinking along the lines of the distributive law, which Mentallic later verified, and I guess it does seem to be pretty much as fundamental as you can go. But, of course, the question of why the distributive law is so can then be raised... Thanks freireib...

That answer might be leading in the right direction...Maybe it will help if I frame the question with reference to the order of operations: WHY does squaring two numbers after they have first been added together produce a result different to when they are squared individually first and then...