When the product of two surds is rational each surd is called a rationalising factor of the other.the process of multiplying a surd by another surd to get a rational number is called rationalization.
rationalizing factor is defined as a homogenous quadratic function of some mathematical symbol. The symbols are as follows. (⋋, ∑, ∍) etc. we see that how a rationalizing factor can be obtained for a given equation. rationalizing factor contain a root higher than a square root. in many cases it is easily obtained by using its conjugate by using the factor expression such as (Xp + yq). 

here is a simpler explanation: the term with which you multiply and divide to make the whole term rational (i.e denominator rational) e.q. rationalising factor for (1/(sqrt(2) - 1) is (sqrt(2) +1 ) as when multiplied and divided by this,, we are left with (sqrt(2) + 1)/1 which is rational.