Square Root Calculator › Square root of 339
Square Root of 339
√339 ≈ 18.411953
339 is not a perfect square, so √339 is an irrational number that is approximately 18.411953. In simplified radical form, √339 = √339.
√339 lies between √324 = 18 and √361 = 19.
| Number | 339 |
| Square root (decimal) | 18.411953 |
| Simplified radical | √339 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 339
339 = 3 × 113. This is what determines the simplified radical: for √339 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √339 is already in simplest radical form as √339.
Estimating √339 by hand
√339 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 339 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.416667 |
| Step 2 | 18.411953 |
| Step 3 | 18.411953 |
After 3 steps the estimate is 18.411953, matching √339 ≈ 18.411953.
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Frequently asked questions
Is 339 a perfect square?
No, 339 is not a perfect square, so its square root is irrational and approximately 18.411953.
What is the square root of 339 in simplest radical form?
√339 = √339 in simplest radical form.