Square Root Calculator › Square root of 119
Square Root of 119
√119 ≈ 10.908712
119 is not a perfect square, so √119 is an irrational number that is approximately 10.908712. In simplified radical form, √119 = √119.
√119 lies between √100 = 10 and √121 = 11.
| Number | 119 |
| Square root (decimal) | 10.908712 |
| Simplified radical | √119 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 119
119 = 7 × 17. This is what determines the simplified radical: for √119 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √119 is already in simplest radical form as √119.
Estimating √119 by hand
√119 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 119 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.95 |
| Step 2 | 10.90879 |
| Step 3 | 10.908712 |
After 3 steps the estimate is 10.908712, matching √119 ≈ 10.908712.
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Frequently asked questions
Is 119 a perfect square?
No, 119 is not a perfect square, so its square root is irrational and approximately 10.908712.
What is the square root of 119 in simplest radical form?
√119 = √119 in simplest radical form.