Square Root Calculator › Square root of 139
Square Root of 139
√139 ≈ 11.789826
139 is not a perfect square, so √139 is an irrational number that is approximately 11.789826. In simplified radical form, √139 = √139.
√139 lies between √121 = 11 and √144 = 12.
| Number | 139 |
| Square root (decimal) | 11.789826 |
| Simplified radical | √139 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 139
139 = 139. This is what determines the simplified radical: for √139 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √139 is already in simplest radical form as √139.
Estimating √139 by hand
√139 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 139 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.818182 |
| Step 2 | 11.78986 |
| Step 3 | 11.789826 |
After 3 steps the estimate is 11.789826, matching √139 ≈ 11.789826.
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Frequently asked questions
Is 139 a perfect square?
No, 139 is not a perfect square, so its square root is irrational and approximately 11.789826.
What is the square root of 139 in simplest radical form?
√139 = √139 in simplest radical form.