Real numbers
Grade Class 10
Question:
<p>According to the Fundamental Theorem of Arithmetic, if p (a prime number) divides b<sup>2</sup> and b is positive, then ________.</p>
<p style="display:inline">p divides b</p>
<p style="display:inline">b divides p</p>
<p style="display:inline">p<sup>2</sup> divides b</p>
<p style="display:inline">b<sup>2</sup> divides p</p>
Step-by-Step Solution
Key Concept: If a prime number divides the square of a positive integer, it must necessarily divide the integer itself as a consequence of unique prime factorization.
<p>If p divides b<sup>2</sup>, then p also divides b.</p>
Correct Answer: A