Square Root Calculator › Square root of 265
Square Root of 265
√265 ≈ 16.278821
265 is not a perfect square, so √265 is an irrational number that is approximately 16.278821. In simplified radical form, √265 = √265.
√265 lies between √256 = 16 and √289 = 17.
| Number | 265 |
| Square root (decimal) | 16.278821 |
| Simplified radical | √265 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 265
265 = 5 × 53. This is what determines the simplified radical: for √265 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √265 is already in simplest radical form as √265.
Estimating √265 by hand
√265 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 265 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.28125 |
| Step 2 | 16.278821 |
| Step 3 | 16.278821 |
After 3 steps the estimate is 16.278821, matching √265 ≈ 16.278821.
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Frequently asked questions
Is 265 a perfect square?
No, 265 is not a perfect square, so its square root is irrational and approximately 16.278821.
What is the square root of 265 in simplest radical form?
√265 = √265 in simplest radical form.