How do you square a number near 100, e.g. 97²?

Add the number's surplus (or subtract its shortfall) to itself for the left part, then append the square of that deviation (two digits).

This is the near-base method with both numbers equal:

• 97² → shortfall 3 → 97 − 3 = 94, and 3² = 09 → 9409.
• 96² → shortfall 4 → 96 − 4 = 92, and 16 → 9216.
• 103² → surplus 3 → 103 + 3 = 106, and 09 → 10609.
• 108² → surplus 8 → 108 + 8 = 116, and 64 → 11664.

Check: 97² = 9409 ✓. From (100 ± d)² = 10000 ± 200d + d² (note 100 − d ⇒ left part is 100 − 2d = the number − d).