Square Root Calculator › Square root of 241
Square Root of 241
√241 ≈ 15.524175
241 is not a perfect square, so √241 is an irrational number that is approximately 15.524175. In simplified radical form, √241 = √241.
√241 lies between √225 = 15 and √256 = 16.
| Number | 241 |
| Square root (decimal) | 15.524175 |
| Simplified radical | √241 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 241
241 = 241. This is what determines the simplified radical: for √241 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √241 is already in simplest radical form as √241.
Estimating √241 by hand
√241 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 241 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.533333 |
| Step 2 | 15.524177 |
| Step 3 | 15.524175 |
After 3 steps the estimate is 15.524175, matching √241 ≈ 15.524175.
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Frequently asked questions
Is 241 a perfect square?
No, 241 is not a perfect square, so its square root is irrational and approximately 15.524175.
What is the square root of 241 in simplest radical form?
√241 = √241 in simplest radical form.