Square Root Calculator › Square root of 391
Square Root of 391
√391 ≈ 19.77372
391 is not a perfect square, so √391 is an irrational number that is approximately 19.77372. In simplified radical form, √391 = √391.
√391 lies between √361 = 19 and √400 = 20.
| Number | 391 |
| Square root (decimal) | 19.77372 |
| Simplified radical | √391 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 391
391 = 17 × 23. This is what determines the simplified radical: for √391 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √391 is already in simplest radical form as √391.
Estimating √391 by hand
√391 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 391 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.789474 |
| Step 2 | 19.773726 |
| Step 3 | 19.77372 |
After 3 steps the estimate is 19.77372, matching √391 ≈ 19.77372.
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Frequently asked questions
Is 391 a perfect square?
No, 391 is not a perfect square, so its square root is irrational and approximately 19.77372.
What is the square root of 391 in simplest radical form?
√391 = √391 in simplest radical form.