If (p^2) is a multiple of 5, prove that p is multiple of 5?

if p² is multiple of 5

that means p² must have 0 or 5 as the last digit

since p x p = p²

that means the square of last digit of p must be 0 or 5

and the only digits whose square is 0 or 5 are 0 and 5

2² = 4, 3² = 9, 4² = 16, last digit 6, and so on

and since we've proved that last digits of p must be 0 or 5 that means p is multiple of 5 as well.

I don't know if this is correct method for which you're looking for but this one is easiest.

let p = 7 (which is not a multiple of 5) , then 7^2 = 49 is also not a multiple of 5

so if p is not a multiple of 5 then , p^2 also is not a multiple of 5

now

if p = 35 which is a multiple of 5 , then p^2 = 35*35 = 1225 which is a multiple of 5

so proved