Square Root Calculator › Square root of 329
Square Root of 329
√329 ≈ 18.138357
329 is not a perfect square, so √329 is an irrational number that is approximately 18.138357. In simplified radical form, √329 = √329.
√329 lies between √324 = 18 and √361 = 19.
| Number | 329 |
| Square root (decimal) | 18.138357 |
| Simplified radical | √329 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 329
329 = 7 × 47. This is what determines the simplified radical: for √329 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √329 is already in simplest radical form as √329.
Estimating √329 by hand
√329 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 329 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.138889 |
| Step 2 | 18.138357 |
| Step 3 | 18.138357 |
After 3 steps the estimate is 18.138357, matching √329 ≈ 18.138357.
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Frequently asked questions
Is 329 a perfect square?
No, 329 is not a perfect square, so its square root is irrational and approximately 18.138357.
What is the square root of 329 in simplest radical form?
√329 = √329 in simplest radical form.