Squaring numbers that end in 5
Take the digits before the 5, multiply them by the next whole number, and write 25 after the result.
35² → 3 × 4 = 12 → 1225 85² → 8 × 9 = 72 → 7225 115² → 11 × 12 = 132 → 13225
Why it works
A number ending in 5 is 10n + 5. Its square is
(10n + 5)² = 100n² + 100n + 25 = 100·n(n + 1) + 25
So the hundreds and above are always n(n + 1), and the last two digits are always 25.
A cousin of the trick
The same algebra works for any two numbers with the same tens digit whose last digits add to ten:
43 × 47 is 4 × 5 = 20, then 3 × 7 = 21, giving 2021.