Question

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

• A. Always a natural number
• B. Always a rational number
• C. Always an irrational number
• D. Either a natural number or a irrational number

Answer 1

Answer: (D)

Either a natural number or a irrational number

Let $n$ be a natural number.
Case I: $n$ is a perfect square $(1,4,9,16,25,....$ etc. $)$
Then $\sqrt{n}$ is a natural number.
$\sqrt{1},\sqrt{4},\sqrt{9},\sqrt{16},\sqrt{25}$, etc. are all natural numbers.
Case II. $n$ is not a perfect square $(2,3,5,6,7,8,....$ etc. $)$
$\sqrt{2},\sqrt{3},\sqrt{5},\sqrt{6},\sqrt{7}$ etc. are all irrational.
Therefore, $\sqrt{n}$ is either a natural number of an irrational number.