How do you square a number near 50, e.g. 47²?

Start from 25; add the amount above 50 (or subtract the amount below) for the first part, then tack on the square of that deviation as the last two digits.

Write the number as 50 ± d. The result is (25 ± d) followed by d² (two digits):

• 47² (d = −3) → 25 − 3 = 22, and (−3)² = 09 → 2209.
• 53² (d = +3) → 25 + 3 = 28, and 3² = 09 → 2809.
• 58² (d = +8) → 25 + 8 = 33, and 8² = 64 → 3364.

Check: 47² = 2209 ✓. It comes from (50 ± d)² = 2500 ± 100d + d².

Pitfall: the d² slot holds two digits — if d² ≥ 100, carry the extra hundreds into the first part.