Square Root Calculator › Square root of 331
Square Root of 331
√331 ≈ 18.193405
331 is not a perfect square, so √331 is an irrational number that is approximately 18.193405. In simplified radical form, √331 = √331.
√331 lies between √324 = 18 and √361 = 19.
| Number | 331 |
| Square root (decimal) | 18.193405 |
| Simplified radical | √331 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 331
331 = 331. This is what determines the simplified radical: for √331 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √331 is already in simplest radical form as √331.
Estimating √331 by hand
√331 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 331 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.194444 |
| Step 2 | 18.193405 |
| Step 3 | 18.193405 |
After 3 steps the estimate is 18.193405, matching √331 ≈ 18.193405.
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Frequently asked questions
Is 331 a perfect square?
No, 331 is not a perfect square, so its square root is irrational and approximately 18.193405.
What is the square root of 331 in simplest radical form?
√331 = √331 in simplest radical form.