Try working out 1 x 142857, 2 x 142857, 3 x 142857, 4 x 142857, 5 x 142857, 6 x 142857. What do you notice? Why does it work?

To find the square of any two-digit number ending in 5 (say 65), take the first digit (6) and multiply it by one more than itself (7) and adjoin 25 to the product (42) and get the required square (4225). Can you explain why this trick works?