Square Root Calculator › Square root of 278
Square Root of 278
√278 ≈ 16.673332
278 is not a perfect square, so √278 is an irrational number that is approximately 16.673332. In simplified radical form, √278 = √278.
√278 lies between √256 = 16 and √289 = 17.
| Number | 278 |
| Square root (decimal) | 16.673332 |
| Simplified radical | √278 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 278
278 = 2 × 139. This is what determines the simplified radical: for √278 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √278 is already in simplest radical form as √278.
Estimating √278 by hand
√278 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 278 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.6875 |
| Step 2 | 16.673338 |
| Step 3 | 16.673332 |
After 3 steps the estimate is 16.673332, matching √278 ≈ 16.673332.
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Frequently asked questions
Is 278 a perfect square?
No, 278 is not a perfect square, so its square root is irrational and approximately 16.673332.
What is the square root of 278 in simplest radical form?
√278 = √278 in simplest radical form.