Square Root Calculator › Square root of 271
Square Root of 271
√271 ≈ 16.462078
271 is not a perfect square, so √271 is an irrational number that is approximately 16.462078. In simplified radical form, √271 = √271.
√271 lies between √256 = 16 and √289 = 17.
| Number | 271 |
| Square root (decimal) | 16.462078 |
| Simplified radical | √271 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 271
271 = 271. This is what determines the simplified radical: for √271 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √271 is already in simplest radical form as √271.
Estimating √271 by hand
√271 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 271 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.46875 |
| Step 2 | 16.462079 |
| Step 3 | 16.462078 |
After 3 steps the estimate is 16.462078, matching √271 ≈ 16.462078.
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Frequently asked questions
Is 271 a perfect square?
No, 271 is not a perfect square, so its square root is irrational and approximately 16.462078.
What is the square root of 271 in simplest radical form?
√271 = √271 in simplest radical form.