Limits by Rationalization Questions with solutions

Evaluating the limits by rationalizing the radical form functions is one type of limits questions in calculus. The limits by rationalization method problems are given here as a worksheet for your practice and the limits by rationalisation questions examples with solutions to learn how to rationalize the irrational functions, to avoid the indeterminate form while finding the limits.

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{x}{\sqrt{x+4}-2}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\sqrt{1+x}-1}{x}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 3}{\normalsize \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize (\sqrt{x^2+2x}-x)}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 4}{\normalsize \dfrac{\sqrt{1+2x}-3}{\sqrt{x}-2}}$