Square Root Calculator › Square root of 267
Square Root of 267
√267 ≈ 16.340135
267 is not a perfect square, so √267 is an irrational number that is approximately 16.340135. In simplified radical form, √267 = √267.
√267 lies between √256 = 16 and √289 = 17.
| Number | 267 |
| Square root (decimal) | 16.340135 |
| Simplified radical | √267 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 267
267 = 3 × 89. This is what determines the simplified radical: for √267 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √267 is already in simplest radical form as √267.
Estimating √267 by hand
√267 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 267 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.34375 |
| Step 2 | 16.340135 |
| Step 3 | 16.340135 |
After 3 steps the estimate is 16.340135, matching √267 ≈ 16.340135.
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Frequently asked questions
Is 267 a perfect square?
No, 267 is not a perfect square, so its square root is irrational and approximately 16.340135.
What is the square root of 267 in simplest radical form?
√267 = √267 in simplest radical form.