Square Root Calculator › Square root of 268
Square Root of 268
√268 ≈ 16.370706
268 is not a perfect square, so √268 is an irrational number that is approximately 16.370706. In simplified radical form, √268 = 2√67.
√268 lies between √256 = 16 and √289 = 17.
| Number | 268 |
| Square root (decimal) | 16.370706 |
| Simplified radical | 2√67 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 268
268 = 2^2 × 67. This is what determines the simplified radical: for √268 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √268 = 2√67.
Estimating √268 by hand
√268 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 268 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.375 |
| Step 2 | 16.370706 |
| Step 3 | 16.370706 |
After 3 steps the estimate is 16.370706, matching √268 ≈ 16.370706.
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Frequently asked questions
Is 268 a perfect square?
No, 268 is not a perfect square, so its square root is irrational and approximately 16.370706.
What is the square root of 268 in simplest radical form?
√268 = 2√67 in simplest radical form.