Square Root Calculator › Square root of 199
Square Root of 199
√199 ≈ 14.106736
199 is not a perfect square, so √199 is an irrational number that is approximately 14.106736. In simplified radical form, √199 = √199.
√199 lies between √196 = 14 and √225 = 15.
| Number | 199 |
| Square root (decimal) | 14.106736 |
| Simplified radical | √199 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 199
199 = 199. This is what determines the simplified radical: for √199 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √199 is already in simplest radical form as √199.
Estimating √199 by hand
√199 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 199 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.107143 |
| Step 2 | 14.106736 |
| Step 3 | 14.106736 |
After 3 steps the estimate is 14.106736, matching √199 ≈ 14.106736.
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Frequently asked questions
Is 199 a perfect square?
No, 199 is not a perfect square, so its square root is irrational and approximately 14.106736.
What is the square root of 199 in simplest radical form?
√199 = √199 in simplest radical form.