If n is a natural number, then
Question:

If $n$ is a natural number, then $\sqrt{n}$ is

(a) always a natural number
(b) always an irrational number
(c) always an irrational number
(d) sometimes a natural number and sometimes an irrational number

Solution:

The term “natural number” refers either to a member of the set of positive integer $1,2,3$.

And natural number starts from one of counting digit. Thus, if $n$ is a natural number then sometimes $n$ is a perfect square and sometimes it is not.

Therefore, sometimes $\sqrt{n}$ is a natural number and sometimes it is an irrational number

Hence the correct option is $d$.

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