Square Root Calculator › Square root of 396
Square Root of 396
√396 ≈ 19.899749
396 is not a perfect square, so √396 is an irrational number that is approximately 19.899749. In simplified radical form, √396 = 6√11.
√396 lies between √361 = 19 and √400 = 20.
| Number | 396 |
| Square root (decimal) | 19.899749 |
| Simplified radical | 6√11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 396
396 = 2^2 × 3^2 × 11. This is what determines the simplified radical: for √396 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √396 = 6√11.
Estimating √396 by hand
√396 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 396 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.921053 |
| Step 2 | 19.89976 |
| Step 3 | 19.899749 |
After 3 steps the estimate is 19.899749, matching √396 ≈ 19.899749.
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Frequently asked questions
Is 396 a perfect square?
No, 396 is not a perfect square, so its square root is irrational and approximately 19.899749.
What is the square root of 396 in simplest radical form?
√396 = 6√11 in simplest radical form.