Express (3 - sqrt(5))^2 in the form m + n*sqrt(5), where m and n are integers.
Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)). Notice that this looks a lot like a factorised quadratic equation, where sqrt(5) can be treated as a variable like x. Therefore, we can expand these brackets in the same way we expand these factorised quadratic equations. Following the same process should result in 9 - 6sqrt(5) + sqrt(5)2 which is equal to 14 - 6sqrt(5). Checking back with the question it where m and n are wanted, n = -6 as it is the coefficient of the term with sqrt(5) and m = 14 as it is the term that is a pure integer.
AP
