SSC CPO Tier 1 Exam 9 Dec 2025 Shift 1

Concept:A prime number has exactly two divisors: 1 and itself. Its square root cannot be written as a fraction of two integers.Explanation:Assume $\sqrt{p}$ is rational, i.e., $\sqrt{p} = \frac{a}{b}$ in lowest terms. Then $p = \frac{a^2}{b^2}$, so $a^2 = p b^2$. This forces $p$ to divide $a$, and repeating shows $p$ divides $b$, contradicting lowest terms. Hence $\sqrt{p}$ is always irrational.Examples: $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$ are all non‑repeating, non‑terminating decimals.Answer:C. Irrational