Square Root Calculator › Square root of 233
Square Root of 233
√233 ≈ 15.264338
233 is not a perfect square, so √233 is an irrational number that is approximately 15.264338. In simplified radical form, √233 = √233.
√233 lies between √225 = 15 and √256 = 16.
| Number | 233 |
| Square root (decimal) | 15.264338 |
| Simplified radical | √233 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 233
233 = 233. This is what determines the simplified radical: for √233 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √233 is already in simplest radical form as √233.
Estimating √233 by hand
√233 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 233 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.266667 |
| Step 2 | 15.264338 |
| Step 3 | 15.264338 |
After 3 steps the estimate is 15.264338, matching √233 ≈ 15.264338.
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Frequently asked questions
Is 233 a perfect square?
No, 233 is not a perfect square, so its square root is irrational and approximately 15.264338.
What is the square root of 233 in simplest radical form?
√233 = √233 in simplest radical form.