Square Root Calculator › Square root of 330
Square Root of 330
√330 ≈ 18.165902
330 is not a perfect square, so √330 is an irrational number that is approximately 18.165902. In simplified radical form, √330 = √330.
√330 lies between √324 = 18 and √361 = 19.
| Number | 330 |
| Square root (decimal) | 18.165902 |
| Simplified radical | √330 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 330
330 = 2 × 3 × 5 × 11. This is what determines the simplified radical: for √330 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √330 is already in simplest radical form as √330.
Estimating √330 by hand
√330 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 330 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.166667 |
| Step 2 | 18.165902 |
| Step 3 | 18.165902 |
After 3 steps the estimate is 18.165902, matching √330 ≈ 18.165902.
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Frequently asked questions
Is 330 a perfect square?
No, 330 is not a perfect square, so its square root is irrational and approximately 18.165902.
What is the square root of 330 in simplest radical form?
√330 = √330 in simplest radical form.