Square Root Calculator › Square root of 228
Square Root of 228
√228 ≈ 15.099669
228 is not a perfect square, so √228 is an irrational number that is approximately 15.099669. In simplified radical form, √228 = 2√57.
√228 lies between √225 = 15 and √256 = 16.
| Number | 228 |
| Square root (decimal) | 15.099669 |
| Simplified radical | 2√57 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 228
228 = 2^2 × 3 × 19. This is what determines the simplified radical: for √228 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √228 = 2√57.
Estimating √228 by hand
√228 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 228 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.1 |
| Step 2 | 15.099669 |
| Step 3 | 15.099669 |
After 3 steps the estimate is 15.099669, matching √228 ≈ 15.099669.
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Frequently asked questions
Is 228 a perfect square?
No, 228 is not a perfect square, so its square root is irrational and approximately 15.099669.
What is the square root of 228 in simplest radical form?
√228 = 2√57 in simplest radical form.