Why we rationalize, conjugate. My question is why we rationalise, conjugate any denominator containing irrational or imaginary quantity. What is the need to rationalize them?

As a tool to solve problems, sometimes it is desirable to do so. For instance,

$$\lim_{x\rightarrow 0} \frac x{\sqrt{x+1}-1} =\lim_{x\rightarrow 0} \frac {x(\sqrt{x+1}+1)}{(\sqrt{x+1}-1)(\sqrt{x+1}+1)} =\lim_{x\rightarrow 0} \frac {x(\sqrt{x+1}+1)}{x} =\lim_{x\rightarrow 0} \sqrt{x+1}+1 =2$$