Square Root Calculator › Square root of 41
Square Root of 41
√41 ≈ 6.403124
41 is not a perfect square, so √41 is an irrational number that is approximately 6.403124. In simplified radical form, √41 = √41.
√41 lies between √36 = 6 and √49 = 7.
| Number | 41 |
| Square root (decimal) | 6.403124 |
| Simplified radical | √41 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 41
41 = 41. This is what determines the simplified radical: for √41 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √41 is already in simplest radical form as √41.
Estimating √41 by hand
√41 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 41 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.416667 |
| Step 2 | 6.403139 |
| Step 3 | 6.403124 |
After 3 steps the estimate is 6.403124, matching √41 ≈ 6.403124.
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Frequently asked questions
Is 41 a perfect square?
No, 41 is not a perfect square, so its square root is irrational and approximately 6.403124.
What is the square root of 41 in simplest radical form?
√41 = √41 in simplest radical form.