Square Root Calculator › Square root of 261
Square Root of 261
√261 ≈ 16.155494
261 is not a perfect square, so √261 is an irrational number that is approximately 16.155494. In simplified radical form, √261 = 3√29.
√261 lies between √256 = 16 and √289 = 17.
| Number | 261 |
| Square root (decimal) | 16.155494 |
| Simplified radical | 3√29 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 261
261 = 3^2 × 29. This is what determines the simplified radical: for √261 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √261 = 3√29.
Estimating √261 by hand
√261 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 261 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.15625 |
| Step 2 | 16.155494 |
| Step 3 | 16.155494 |
After 3 steps the estimate is 16.155494, matching √261 ≈ 16.155494.
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Frequently asked questions
Is 261 a perfect square?
No, 261 is not a perfect square, so its square root is irrational and approximately 16.155494.
What is the square root of 261 in simplest radical form?
√261 = 3√29 in simplest radical form.