Square Root Calculator › Square root of 611
Square Root of 611
√611 ≈ 24.718414
611 is not a perfect square, so √611 is an irrational number that is approximately 24.718414. In simplified radical form, √611 = √611.
√611 lies between √576 = 24 and √625 = 25.
| Number | 611 |
| Square root (decimal) | 24.718414 |
| Simplified radical | √611 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 611
611 = 13 × 47. This is what determines the simplified radical: for √611 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √611 is already in simplest radical form as √611.
Estimating √611 by hand
√611 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 611 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.729167 |
| Step 2 | 24.718417 |
| Step 3 | 24.718414 |
After 3 steps the estimate is 24.718414, matching √611 ≈ 24.718414.
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Frequently asked questions
Is 611 a perfect square?
No, 611 is not a perfect square, so its square root is irrational and approximately 24.718414.
What is the square root of 611 in simplest radical form?
√611 = √611 in simplest radical form.