Square Root Calculator › Square root of 371
Square Root of 371
√371 ≈ 19.26136
371 is not a perfect square, so √371 is an irrational number that is approximately 19.26136. In simplified radical form, √371 = √371.
√371 lies between √361 = 19 and √400 = 20.
| Number | 371 |
| Square root (decimal) | 19.26136 |
| Simplified radical | √371 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 371
371 = 7 × 53. This is what determines the simplified radical: for √371 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √371 is already in simplest radical form as √371.
Estimating √371 by hand
√371 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 371 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.263158 |
| Step 2 | 19.26136 |
| Step 3 | 19.26136 |
After 3 steps the estimate is 19.26136, matching √371 ≈ 19.26136.
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Frequently asked questions
Is 371 a perfect square?
No, 371 is not a perfect square, so its square root is irrational and approximately 19.26136.
What is the square root of 371 in simplest radical form?
√371 = √371 in simplest radical form.