Square Root Calculator › Square root of 232
Square Root of 232
√232 ≈ 15.231546
232 is not a perfect square, so √232 is an irrational number that is approximately 15.231546. In simplified radical form, √232 = 2√58.
√232 lies between √225 = 15 and √256 = 16.
| Number | 232 |
| Square root (decimal) | 15.231546 |
| Simplified radical | 2√58 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 232
232 = 2^3 × 29. This is what determines the simplified radical: for √232 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √232 = 2√58.
Estimating √232 by hand
√232 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 232 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.233333 |
| Step 2 | 15.231546 |
| Step 3 | 15.231546 |
After 3 steps the estimate is 15.231546, matching √232 ≈ 15.231546.
Nearby square roots
Frequently asked questions
Is 232 a perfect square?
No, 232 is not a perfect square, so its square root is irrational and approximately 15.231546.
What is the square root of 232 in simplest radical form?
√232 = 2√58 in simplest radical form.