Square Root Calculator › Square root of 250
Square Root of 250
√250 ≈ 15.811388
250 is not a perfect square, so √250 is an irrational number that is approximately 15.811388. In simplified radical form, √250 = 5√10.
√250 lies between √225 = 15 and √256 = 16.
| Number | 250 |
| Square root (decimal) | 15.811388 |
| Simplified radical | 5√10 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 250
250 = 2 × 5^3. This is what determines the simplified radical: for √250 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √250 = 5√10.
Estimating √250 by hand
√250 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 250 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.833333 |
| Step 2 | 15.811404 |
| Step 3 | 15.811388 |
After 3 steps the estimate is 15.811388, matching √250 ≈ 15.811388.
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Frequently asked questions
Is 250 a perfect square?
No, 250 is not a perfect square, so its square root is irrational and approximately 15.811388.
What is the square root of 250 in simplest radical form?
√250 = 5√10 in simplest radical form.