Question

$2\sqrt{5}$ is
(a) an integer
(b) a irrational number
(c) a rational number
(d) none of these

Answer 1

(b) an irrational number

$2\sqrt{5}$ is an irrational number.
Proof: Let $2\sqrt{5}$ be rational.
∴$\frac{1}{2}\times 2\sqrt{5}$ = $\sqrt{5}$ [∵ Product of two rational is rational]
∴ $\sqrt{5}$ is rational, which is not true (As 5 is prime, $\sqrt{5}$ is an irrational number)
Hence, $\sqrt{5}$ is an irrational number.