Square Root Calculator › Square root of 327
Square Root of 327
√327 ≈ 18.083141
327 is not a perfect square, so √327 is an irrational number that is approximately 18.083141. In simplified radical form, √327 = √327.
√327 lies between √324 = 18 and √361 = 19.
| Number | 327 |
| Square root (decimal) | 18.083141 |
| Simplified radical | √327 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 327
327 = 3 × 109. This is what determines the simplified radical: for √327 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √327 is already in simplest radical form as √327.
Estimating √327 by hand
√327 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 327 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.083333 |
| Step 2 | 18.083141 |
| Step 3 | 18.083141 |
After 3 steps the estimate is 18.083141, matching √327 ≈ 18.083141.
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Frequently asked questions
Is 327 a perfect square?
No, 327 is not a perfect square, so its square root is irrational and approximately 18.083141.
What is the square root of 327 in simplest radical form?
√327 = √327 in simplest radical form.