What are surds and how do I use them ?

Surds are irrational numbers, (numbers which cannot be expressed as fractions), and normally shown as a number instead a square root, but the number itself isn't a square. For example root 3 is a surd, while root 4 is not as it equals 2. Well how do I use these numbers ? Well they do look pretty weird but how you deal with them is fairly easy once you follow these simple rules! 1) Larger surds can be broken down into multiple smaller surds, or real numbers ! This makes life a lot simpler as you are dealing with much smaller numbers.2)A fraction which is completely in a square root, can be re-written as both the numerator and the denominator both being surds( i.e surd/surd). This means that this new format can be simplified by using rule 1 !3)If you have two surds in addition, with the same root (e.g y root(x) + z root(x) ), it can be simplified and written as (y+z) root(x).4)If you have a surd in the form of x / root(y), you can rationalise the denominator by multiplying top and bottom of the fraction by root (y) , to get x root(y) / y. This value is far easier to work with, and gives us the simplified final answer. Similarly surds where the denominator contains more than just the surd (i.e a + root(b) ), this can be rationalised as well, by multiplying by a - root (b) .