Square Root Calculator › Square root of 341
Square Root of 341
√341 ≈ 18.466185
341 is not a perfect square, so √341 is an irrational number that is approximately 18.466185. In simplified radical form, √341 = √341.
√341 lies between √324 = 18 and √361 = 19.
| Number | 341 |
| Square root (decimal) | 18.466185 |
| Simplified radical | √341 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 341
341 = 11 × 31. This is what determines the simplified radical: for √341 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √341 is already in simplest radical form as √341.
Estimating √341 by hand
√341 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 341 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.472222 |
| Step 2 | 18.466186 |
| Step 3 | 18.466185 |
After 3 steps the estimate is 18.466185, matching √341 ≈ 18.466185.
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Frequently asked questions
Is 341 a perfect square?
No, 341 is not a perfect square, so its square root is irrational and approximately 18.466185.
What is the square root of 341 in simplest radical form?
√341 = √341 in simplest radical form.