Square of 9
9 squared equals 81. Squares appear in area calculations, the Pythagorean theorem, and statistics (variance uses squared distances).
Squares obey quiet rules. Divided by 9, a square only ever leaves 0, 1, 4 or 7 — 0 here. On the last digit, squares end only in 0, 1, 4, 5, 6 or 9, and 1 fits. Between its neighbors, 64 sits 17 below and 100 sits 19 above — the square ladder widens by exactly two at every step. An odd base keeps the square odd: 81 ends in an odd digit, as every odd square must. Two anchors most worth memorizing in this range are 12² = 144 and 15² = 225 — the odd-step rule above is why knowing them pays off, because from any anchor the next square is one step along this page's ladder.
| Expression | Value |
|---|---|
| 9² | 81 |
Frequently asked questions
What is 9 squared?
9 squared is 81, because 9 × 9 = 81. The exponent 2 is why it is written 9².
What is 10 squared, next to 9²?
10² = 100, which is 19 more than 9² = 81. Each step up adds double the base plus one.
Where do squares show up in real problems?
Area of a square with side 9, distance in the Pythagorean theorem, and variance in statistics all use squared values.