Square Root Calculator › Square root of 234
Square Root of 234
√234 ≈ 15.297059
234 is not a perfect square, so √234 is an irrational number that is approximately 15.297059. In simplified radical form, √234 = 3√26.
√234 lies between √225 = 15 and √256 = 16.
| Number | 234 |
| Square root (decimal) | 15.297059 |
| Simplified radical | 3√26 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 234
234 = 2 × 3^2 × 13. This is what determines the simplified radical: for √234 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √234 = 3√26.
Estimating √234 by hand
√234 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 234 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.3 |
| Step 2 | 15.297059 |
| Step 3 | 15.297059 |
After 3 steps the estimate is 15.297059, matching √234 ≈ 15.297059.
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Frequently asked questions
Is 234 a perfect square?
No, 234 is not a perfect square, so its square root is irrational and approximately 15.297059.
What is the square root of 234 in simplest radical form?
√234 = 3√26 in simplest radical form.