The above diagram has been taken from our “Fractions and recurring decimals” tutorial (if you haven’t read it, make sure you do). We can see from the diagram that surds are non-repeating and are thus irrational numbers which cannot be turned into a fraction.
The most common surds you will meet are √2, √3,√5, √(7,) √10, √11,√13, √(15, ) √17, √19,√21, √(22,) √23, √26,√29 and √(30, ) but there are many more and the most important thing is to understand the theory behind how to work with them rather than memorising the list above. Just like in the tutorial “Basic Algebra, formulae and substitution”, surds can be thought to behave like a term in an expression. However, instead of having an unknown value (e.g. x), we have an irrational number. This means they can be added, subtracted, multiplied and divided in a very specific way. Let’s delve right in…
Use the formulae m×√a≡m√a and m√a±n√a≡(m±n) √a