√5 is rational (contradiction method)
√5=a/b (a and b are not common factor)
5=a^2/b^2 (squaring both sides)
a^2=25 b^2, ( a=5c)
But now we find that 5 divides both a and b, which contradicts our earlier assumption that a and b have no common factor.
Therefore, we conclude that our assumption that √5 is rational is false, ie, √5 is irrational.