Square Root Calculator › Square root of 260
Square Root of 260
√260 ≈ 16.124515
260 is not a perfect square, so √260 is an irrational number that is approximately 16.124515. In simplified radical form, √260 = 2√65.
√260 lies between √256 = 16 and √289 = 17.
| Number | 260 |
| Square root (decimal) | 16.124515 |
| Simplified radical | 2√65 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 260
260 = 2^2 × 5 × 13. This is what determines the simplified radical: for √260 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √260 = 2√65.
Estimating √260 by hand
√260 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 260 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.125 |
| Step 2 | 16.124516 |
| Step 3 | 16.124515 |
After 3 steps the estimate is 16.124515, matching √260 ≈ 16.124515.
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Frequently asked questions
Is 260 a perfect square?
No, 260 is not a perfect square, so its square root is irrational and approximately 16.124515.
What is the square root of 260 in simplest radical form?
√260 = 2√65 in simplest radical form.