Can you explain rationalising surds?

Rationalising surds is the process of removing a square root from the bottom of a fraction. The way we do it is by using a little trick involving the difference of two squares.The difference of two squares is a way that we can factorise an expression of the form a² - b² as (a+b)(a-b).
So if we have an irrational number as the denominator of our fraction, we can apply this in reverse to remove the square root. It's easier to see it in action:
Say I have an irrational number such as 1/(1-(sqrt2)) - (sqrt2 is the square root of 2)
Then I can observe that the denominator is of the form a-b, where a = 1, b = sqrt 2.
Knowing this, I can use the difference of two squares in reverse by multiplying our irrational number by (a+b)/(a+b) (as this equals 1 so we aren't changing the value of the original irrational number).
The denominator then becomes a² - b² or -1 in this case, and our numerator becomes a+b, or 1 + sqrt 2.Our original number is now equal to -1 - sqrt 2. We have removed the denominator entirely, and in doing so made it much easier to work with.
1 / (1 - sqrt 2) = -1 - sqrt 2.
(It's much easier to explain with diagrams!)