Square Root Calculator › Square root of 229
Square Root of 229
√229 ≈ 15.132746
229 is not a perfect square, so √229 is an irrational number that is approximately 15.132746. In simplified radical form, √229 = √229.
√229 lies between √225 = 15 and √256 = 16.
| Number | 229 |
| Square root (decimal) | 15.132746 |
| Simplified radical | √229 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 229
229 = 229. This is what determines the simplified radical: for √229 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √229 is already in simplest radical form as √229.
Estimating √229 by hand
√229 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 229 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.133333 |
| Step 2 | 15.132746 |
| Step 3 | 15.132746 |
After 3 steps the estimate is 15.132746, matching √229 ≈ 15.132746.
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Frequently asked questions
Is 229 a perfect square?
No, 229 is not a perfect square, so its square root is irrational and approximately 15.132746.
What is the square root of 229 in simplest radical form?
√229 = √229 in simplest radical form.