Square Root Calculator › Square root of 279
Square Root of 279
√279 ≈ 16.703293
279 is not a perfect square, so √279 is an irrational number that is approximately 16.703293. In simplified radical form, √279 = 3√31.
√279 lies between √256 = 16 and √289 = 17.
| Number | 279 |
| Square root (decimal) | 16.703293 |
| Simplified radical | 3√31 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 279
279 = 3^2 × 31. This is what determines the simplified radical: for √279 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √279 = 3√31.
Estimating √279 by hand
√279 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 279 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.71875 |
| Step 2 | 16.7033 |
| Step 3 | 16.703293 |
After 3 steps the estimate is 16.703293, matching √279 ≈ 16.703293.
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Frequently asked questions
Is 279 a perfect square?
No, 279 is not a perfect square, so its square root is irrational and approximately 16.703293.
What is the square root of 279 in simplest radical form?
√279 = 3√31 in simplest radical form.