Square Root Calculator › Square root of 266
Square Root of 266
√266 ≈ 16.309506
266 is not a perfect square, so √266 is an irrational number that is approximately 16.309506. In simplified radical form, √266 = √266.
√266 lies between √256 = 16 and √289 = 17.
| Number | 266 |
| Square root (decimal) | 16.309506 |
| Simplified radical | √266 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 266
266 = 2 × 7 × 19. This is what determines the simplified radical: for √266 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √266 is already in simplest radical form as √266.
Estimating √266 by hand
√266 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 266 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.3125 |
| Step 2 | 16.309507 |
| Step 3 | 16.309506 |
After 3 steps the estimate is 16.309506, matching √266 ≈ 16.309506.
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Frequently asked questions
Is 266 a perfect square?
No, 266 is not a perfect square, so its square root is irrational and approximately 16.309506.
What is the square root of 266 in simplest radical form?
√266 = √266 in simplest radical form.