Square Root Calculator › Square root of 129
Square Root of 129
√129 ≈ 11.357817
129 is not a perfect square, so √129 is an irrational number that is approximately 11.357817. In simplified radical form, √129 = √129.
√129 lies between √121 = 11 and √144 = 12.
| Number | 129 |
| Square root (decimal) | 11.357817 |
| Simplified radical | √129 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 129
129 = 3 × 43. This is what determines the simplified radical: for √129 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √129 is already in simplest radical form as √129.
Estimating √129 by hand
√129 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 129 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.363636 |
| Step 2 | 11.357818 |
| Step 3 | 11.357817 |
After 3 steps the estimate is 11.357817, matching √129 ≈ 11.357817.
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Frequently asked questions
Is 129 a perfect square?
No, 129 is not a perfect square, so its square root is irrational and approximately 11.357817.
What is the square root of 129 in simplest radical form?
√129 = √129 in simplest radical form.