Square Root Calculator › Square root of 349
Square Root of 349
√349 ≈ 18.681542
349 is not a perfect square, so √349 is an irrational number that is approximately 18.681542. In simplified radical form, √349 = √349.
√349 lies between √324 = 18 and √361 = 19.
| Number | 349 |
| Square root (decimal) | 18.681542 |
| Simplified radical | √349 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 349
349 = 349. This is what determines the simplified radical: for √349 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √349 is already in simplest radical form as √349.
Estimating √349 by hand
√349 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 349 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.694444 |
| Step 2 | 18.681546 |
| Step 3 | 18.681542 |
After 3 steps the estimate is 18.681542, matching √349 ≈ 18.681542.
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Frequently asked questions
Is 349 a perfect square?
No, 349 is not a perfect square, so its square root is irrational and approximately 18.681542.
What is the square root of 349 in simplest radical form?
√349 = √349 in simplest radical form.