Square Root Calculator › Square root of 251
Square Root of 251
√251 ≈ 15.84298
251 is not a perfect square, so √251 is an irrational number that is approximately 15.84298. In simplified radical form, √251 = √251.
√251 lies between √225 = 15 and √256 = 16.
| Number | 251 |
| Square root (decimal) | 15.84298 |
| Simplified radical | √251 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 251
251 = 251. This is what determines the simplified radical: for √251 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √251 is already in simplest radical form as √251.
Estimating √251 by hand
√251 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 251 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.866667 |
| Step 2 | 15.842997 |
| Step 3 | 15.84298 |
After 3 steps the estimate is 15.84298, matching √251 ≈ 15.84298.
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Frequently asked questions
Is 251 a perfect square?
No, 251 is not a perfect square, so its square root is irrational and approximately 15.84298.
What is the square root of 251 in simplest radical form?
√251 = √251 in simplest radical form.