For any prime number p, if p divides $a^2$, where a is any real number then p also divides

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## Model Answer **Option A: $a$** By Theorem 1.2, if $p$ is a prime and $p$ divides $a^2$, then $p$ divides $a$, where $a$ is a positive integer. Source: Chapter 1, Section 1.3 (Theorem 1.2) ## Explanation This is a direct application of **Theorem 1.2** from the textbook. The theorem states specifically that if a prime $p$ divides $a^2$, it must divide $a$ itself (not any fractional power of $a$). The other options involve fractional indices which are not integers, so the theorem does not apply to them. For MCQs like this, simply recall the exact theorem statement.

Mathematics — Standard (041) — CBSE Class 10 board question