Square Root Calculator › Square root of 127
Square Root of 127
√127 ≈ 11.269428
127 is not a perfect square, so √127 is an irrational number that is approximately 11.269428. In simplified radical form, √127 = √127.
√127 lies between √121 = 11 and √144 = 12.
| Number | 127 |
| Square root (decimal) | 11.269428 |
| Simplified radical | √127 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 127
127 = 127. This is what determines the simplified radical: for √127 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √127 is already in simplest radical form as √127.
Estimating √127 by hand
√127 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 127 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.272727 |
| Step 2 | 11.269428 |
| Step 3 | 11.269428 |
After 3 steps the estimate is 11.269428, matching √127 ≈ 11.269428.
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Frequently asked questions
Is 127 a perfect square?
No, 127 is not a perfect square, so its square root is irrational and approximately 11.269428.
What is the square root of 127 in simplest radical form?
√127 = √127 in simplest radical form.