Question

Let p be a prime number if p divides asquare then p divides a where a is a positive integer

Answer 1

this is theorem 1.3 of class 10 ncert.
proof is not in syllabus
this theorem is used to prove a number irrational.
thank you

Answer 2

P divides A square , :. let prime factorisation of A square is : A = P1×P2×P3×P4.......Pn , :. prime factorisation of A square will be A square=(P1×P2....Pn)( P1×P2......Pn). P divides A square (given) :. P is one of P1 P2... , and A= P1×P2....(as above) ,thus P also divides A