Square Any Number Ending in 5 in Your Head (35², 75²…)

Step by step

1. 15² = 225 · 35² = 1225 · 75² = 5625 · pattern?
   Fifteen squared is two twenty-five. Thirty-five squared is twelve twenty-five. Seventy-five squared is fifty-six twenty-five. Spot the pattern?
2. Ends in 25 · front = tens digit × next number
   They all end in twenty-five. And the front is the tens digit times the next number up: one times two, three times four, seven times eight.
3. Way 1: a square patio, 15 ft on each side
   Why does it work? Way one: picture a square patio, fifteen feet on each side.
4. 15 = 10 + 5 → big square, two strips, a 5 × 5 corner
   Split each side into ten and five. That gives a big square, two strips, and a little five-by-five corner.
5. Move a strip to the top → 10 × 20, plus the corner
   Move this strip up to the top. Now the big part is a rectangle, ten by twenty, and the little corner is still there.
6. 10 × 20 + 25 = 225 · 1 × 2 → the 2 hundreds
   Ten times twenty is two hundred, plus the corner's twenty-five: two twenty-five! One times two gave us the two hundreds.
7. 35² = 30 × 40 + 25 = 1225
   Thirty-five works the same way: thirty by forty, plus twenty-five. Three times four is twelve, so it's twelve hundred and twenty-five.
8. Way 2: (30 + 5) × (30 + 5), multiply each part
   Way two is school algebra. Thirty-five squared is thirty plus five, times thirty plus five. Multiply each part.
9. 900 + 150 + 150 + 25 = 1200 + 25
   Nine hundred, plus one fifty, plus one fifty, plus twenty-five. The two one-fifties make three hundred, so nine hundred grows to twelve hundred. Then add the twenty-five!
10. Tens digit × next number, then write 25
    So for any number ending in five: multiply the tens digit by the next number up, then write twenty-five.
11. On a test: (30 + 5)² = 30 × 40 + 25 = 1225
    On a test, write it like this. Thirty-five is thirty plus five. Multiply each part. The middle parts make thirty times ten, so it's thirty times forty. Add twenty-five: twelve twenty-five.