The square root of 1000 is 31.6227766 (rounded to 8 decimal places).
The square root of 1000 is 31.6227766 (rounded to 8 decimal places).
It is not a perfect square, so the root is irrational. In simplest radical form, √1000 = 10√10, because 1000 = 100 × 10.
1000 lies between the perfect squares 961 (31²) and 1024 (32²), so √1000 is between 31 and 32. Our answer 31.6227766 fits that range.
You can check it by squaring the result: 31.6227766² ≈ 1000.
| √1000 | = 31.6227766 |
| 31.6227766² | = 1000 |
| ∛1000 | = 10 |
| Number | Square root | Note |
|---|---|---|
| 289 | 17 | perfect square |
| 324 | 18 | perfect square |
| 361 | 19 | perfect square |
| 400 | 20 | perfect square |
| 500 | 22.36068 | |
| 625 | 25 | perfect square |
| 900 | 30 | perfect square |
| 1000 | 31.622777 | this page |
The square root of 1000 is 31.6227766 (rounded to 8 decimal places).
No. The nearest perfect squares are 961 and 1024.
Irrational. Its decimal never ends or repeats.
The cube root of 1000 is about 10.
Yes. Use the calculator on this page, or open the full free Scientific Calculator with memory, history and keyboard support.