Square Root Calculator › Square root of 231
Square Root of 231
√231 ≈ 15.198684
231 is not a perfect square, so √231 is an irrational number that is approximately 15.198684. In simplified radical form, √231 = √231.
√231 lies between √225 = 15 and √256 = 16.
| Number | 231 |
| Square root (decimal) | 15.198684 |
| Simplified radical | √231 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 231
231 = 3 × 7 × 11. This is what determines the simplified radical: for √231 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √231 is already in simplest radical form as √231.
Estimating √231 by hand
√231 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 231 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.2 |
| Step 2 | 15.198684 |
| Step 3 | 15.198684 |
After 3 steps the estimate is 15.198684, matching √231 ≈ 15.198684.
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Frequently asked questions
Is 231 a perfect square?
No, 231 is not a perfect square, so its square root is irrational and approximately 15.198684.
What is the square root of 231 in simplest radical form?
√231 = √231 in simplest radical form.