Square Root Calculator › Square root of 276
Square Root of 276
√276 ≈ 16.613248
276 is not a perfect square, so √276 is an irrational number that is approximately 16.613248. In simplified radical form, √276 = 2√69.
√276 lies between √256 = 16 and √289 = 17.
| Number | 276 |
| Square root (decimal) | 16.613248 |
| Simplified radical | 2√69 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 276
276 = 2^2 × 3 × 23. This is what determines the simplified radical: for √276 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √276 = 2√69.
Estimating √276 by hand
√276 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 276 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.625 |
| Step 2 | 16.613252 |
| Step 3 | 16.613248 |
After 3 steps the estimate is 16.613248, matching √276 ≈ 16.613248.
Nearby square roots
Frequently asked questions
Is 276 a perfect square?
No, 276 is not a perfect square, so its square root is irrational and approximately 16.613248.
What is the square root of 276 in simplest radical form?
√276 = 2√69 in simplest radical form.