Squaring Spree

Technique: Square any 2-digit number

Numbers ending in 5

Multiply the tens digit by (tens+1), then append 25:

• 35² → 3 × 4 = 12, append 25 → 1225
• 85² → 8 × 9 = 72, append 25 → 7225
• 65² → 6 × 7 = 42, append 25 → 4225

All other numbers — difference of squares

Round to the nearest multiple of 10. Call the distance d. Then: (a+d)(a−d) + d²

• 41² → d=1. 40 × 42 = 1680, + 1² = 1681
• 23² → d=3. 20 × 26 = 520, + 3² = 9, total 529
• 48² → d=2. 46 × 50 = 2300, + 2² = 4, total 2304

Why does this work?

a² = (a+d)(a−d) + d² is the algebraic identity for the difference of squares. Rounding to a multiple of 10 makes the first multiplication easy.

Every question has a 30 second shot clock.