Square Root Calculator › Square root of 269
Square Root of 269
√269 ≈ 16.401219
269 is not a perfect square, so √269 is an irrational number that is approximately 16.401219. In simplified radical form, √269 = √269.
√269 lies between √256 = 16 and √289 = 17.
| Number | 269 |
| Square root (decimal) | 16.401219 |
| Simplified radical | √269 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 269
269 = 269. This is what determines the simplified radical: for √269 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √269 is already in simplest radical form as √269.
Estimating √269 by hand
√269 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 269 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.40625 |
| Step 2 | 16.40122 |
| Step 3 | 16.401219 |
After 3 steps the estimate is 16.401219, matching √269 ≈ 16.401219.
Nearby square roots
Frequently asked questions
Is 269 a perfect square?
No, 269 is not a perfect square, so its square root is irrational and approximately 16.401219.
What is the square root of 269 in simplest radical form?
√269 = √269 in simplest radical form.