Maths: Roots - simplifying

Yes! I understand that part now hurray , but why does that cancel out?

-6√3+6√3 hmm confuses me I dont get why it cancels out

Consider 1 - 1 = 0

Multiply through by 6√3 (a constant)

$(1\times 6\sqrt3) - (1\times6\sqrt3) = (0\times6\sqrt3)$

$6\sqrt3 - 6\sqrt3 = 0$

Consider 1 - 1 = 0

Multiply through by 6√3 (a constant)

$(1\times 6\sqrt3) - (1\times6\sqrt3) = (0\times6\sqrt3)$

$6\sqrt3 - 6\sqrt3 = 0$

There is an invisible 1 after the - sign in the fist place so it's basically -1 x sqrt3. I think, that's what my teacher told me

Thanks good sir , (yet it still confuses me where the - came from between the 6√3's,) i dont quite understand it yet but thanks for trying.

Sorry, needed the formula thing you used, how do you do that anyway?

Thanks good sir , (yet it still confuses me where the - came from between the 6√3's,) i dont quite understand it yet but thanks for trying.

Yes! I understand that part now hurray , but why does that cancel out?

-6√3+6√3 hmm confuses me I dont get why it cancels out

Okay, it seems everyone else is failing... drastic measures.

What we have discerned:

36 - 6√3 + 6√3 - 3

If you're OK with this part and how we've gotten it so far, read on. If not, no point in reading on, quote this post and ask how we got there.

Now here comes the radical part: forget about the whole √3 thing for a minute. Let x = √3.

Thus you now have:

36 - 6x + 6x - 3

You should know from the most basic algebra lessons you've had that -6x +6x is equal to 0x. I.e. 0. Thus it all cancels out, and all you need is the 36 - 3 (which, obviously, equals 33). For all intents and purposes, surds can be manipulated in a similar manner to algebraic expressions. This is because, as people have pointed out, surds are treated like any other integers.

Are you any closer to understanding it?

HURRRAAAAY HALLELUJAH. I thank you good sir. and Exos who also helped me finally I understand it! I want to get A for maths so I should be better than this, Im just not in the right state of mind at the moment. Be at rest fellow posters, for I have understood.

I'm trying to learn Surds but its tricky and way too many roots everywhere, and I'm confused at simplifying.

Here's the question:

Work out: (6+√ 3)(6-√3) / √ 33
Give your answer in its simplest form.
I've worked out the top part of the equation. 36 - 6√ 3 + 6√ 3 - 3
Now how do I simplify it I'm confused, please tell me how to simplify it.
And any tips on Surds it's really confusing.

Sorry about the title I forgot to put 'Surds' in.