If n is a positive integer, and n^2 has 25 factors, which of the following must be true.
1. n has 12 factors.
2. n > 50
3.√n is an integer.  Choose the correct choice from the following options:
A) 1 and 2  B) 2 only  C) 3 only  D) 2 and 3  E) none
25=1×25=5×5   So prime factorization of n^2 could be p^24 or p^4q^4 with p,q are distinct prime numbers.   Hence, n could be p^12 or p^2q^2   (1) If n=p12 then n has 12+1= 
<gadget id="calculator">12+1</gadget>
<output>13</output>
13 different factors, so (1) is not true.   (2) If n=p^2q^2 , for example n=2^2×3^2=36&lt;50n=22×32=36&lt;50, so (2) is not true.   (3)   If n=p^12 ⟹√n=p^6 is an integer.   If n=p^2q^2 ⟹√n=pq is an integer.   So (3) is true.   Answer: 3 only.
<result>C</result>
If n is a positive integer, and n^2 has 25 factors, which of the following must be true.
1. n has 12 factors.
2. n > 50
3.√n is an integer.