√1000 ≈ 31.6228
√1000 is an irrational number, so its decimals never end or repeat. It sits between 31 and 32 because 31² = 961 and 32² = 1024.
| Decimal places | Value |
|---|---|
| 0 | 32 |
| 1 | 31.6 |
| 2 | 31.62 |
| 3 | 31.623 |
| 4 | 31.6228 |
| 5 | 31.62278 |
| 10 (digits) | 31.6227766017 |
1000 = 100 × 10 and √100 = 10, so √1000 = 10√10.
31.6228 × 31.6228 ≈ 1000.0015, which is very close to 1000.
Need another number? Use the square root calculator (also cube roots and other roots).
| Number | Square root |
|---|---|
| 500 | 22.3607 |
| 529 | 23 |
| 625 | 25 |
| 900 | 30 |