Square Root Calculator › Square root of 227
Square Root of 227
√227 ≈ 15.066519
227 is not a perfect square, so √227 is an irrational number that is approximately 15.066519. In simplified radical form, √227 = √227.
√227 lies between √225 = 15 and √256 = 16.
| Number | 227 |
| Square root (decimal) | 15.066519 |
| Simplified radical | √227 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 227
227 = 227. This is what determines the simplified radical: for √227 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √227 is already in simplest radical form as √227.
Estimating √227 by hand
√227 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 227 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.066667 |
| Step 2 | 15.066519 |
| Step 3 | 15.066519 |
After 3 steps the estimate is 15.066519, matching √227 ≈ 15.066519.
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Frequently asked questions
Is 227 a perfect square?
No, 227 is not a perfect square, so its square root is irrational and approximately 15.066519.
What is the square root of 227 in simplest radical form?
√227 = √227 in simplest radical form.