Square Root Calculator › Square root of 399
Square Root of 399
√399 ≈ 19.974984
399 is not a perfect square, so √399 is an irrational number that is approximately 19.974984. In simplified radical form, √399 = √399.
√399 lies between √361 = 19 and √400 = 20.
| Number | 399 |
| Square root (decimal) | 19.974984 |
| Simplified radical | √399 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 399
399 = 3 × 7 × 19. This is what determines the simplified radical: for √399 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √399 is already in simplest radical form as √399.
Estimating √399 by hand
√399 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 399 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 20 |
| Step 2 | 19.975 |
| Step 3 | 19.974984 |
After 3 steps the estimate is 19.974984, matching √399 ≈ 19.974984.
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Frequently asked questions
Is 399 a perfect square?
No, 399 is not a perfect square, so its square root is irrational and approximately 19.974984.
What is the square root of 399 in simplest radical form?
√399 = √399 in simplest radical form.