If a and b are two distinct natural numbers, which one of the following is true ?

A. $$\sqrt {a + b} > \sqrt a + \sqrt b $$

B. $$\sqrt {a + b} = \sqrt a + \sqrt b $$

C. $$\sqrt {a + b} < \sqrt a + \sqrt b $$

D. $$ab = 1$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \sqrt {a + b\,} \,{\text{and }}\sqrt a + \sqrt b \cr & {\text{Squaring both sides}} \cr & {(\sqrt {a + b\,} )^2}{\text{and (}}\sqrt a + \sqrt b {)^2} \cr & \Rightarrow a + b\,\,{\text{and}}\,a + b + 2\sqrt a \sqrt b \cr & So\,\sqrt {a + b\,} \, < {\text{ }}\sqrt a + \sqrt b \cr} $$