Question

$\sqrt{12}$ is
(a) an integer
(b) a rational number
(c) an irrational number
(d) none of these

Answer 1

(c) an irrational number

$\sqrt{12}=\sqrt{2\times 2\times 3}=2\sqrt{3}$
It is an irrational number.
Proof: Let $2\sqrt{3}$ be rational.
∴ $\frac{1}{2}\times 2\sqrt{3}$ = $\sqrt{3}$ = rational (false)
Hence, $\sqrt{3}$ is an irrational number.