Square Root Calculator › Square root of 191
Square Root of 191
√191 ≈ 13.820275
191 is not a perfect square, so √191 is an irrational number that is approximately 13.820275. In simplified radical form, √191 = √191.
√191 lies between √169 = 13 and √196 = 14.
| Number | 191 |
| Square root (decimal) | 13.820275 |
| Simplified radical | √191 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 191
191 = 191. This is what determines the simplified radical: for √191 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √191 is already in simplest radical form as √191.
Estimating √191 by hand
√191 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 191 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.846154 |
| Step 2 | 13.820299 |
| Step 3 | 13.820275 |
After 3 steps the estimate is 13.820275, matching √191 ≈ 13.820275.
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Frequently asked questions
Is 191 a perfect square?
No, 191 is not a perfect square, so its square root is irrational and approximately 13.820275.
What is the square root of 191 in simplest radical form?
√191 = √191 in simplest radical form.