Square Root Calculator › Square root of 390
Square Root of 390
√390 ≈ 19.748418
390 is not a perfect square, so √390 is an irrational number that is approximately 19.748418. In simplified radical form, √390 = √390.
√390 lies between √361 = 19 and √400 = 20.
| Number | 390 |
| Square root (decimal) | 19.748418 |
| Simplified radical | √390 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 390
390 = 2 × 3 × 5 × 13. This is what determines the simplified radical: for √390 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √390 is already in simplest radical form as √390.
Estimating √390 by hand
√390 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 390 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.763158 |
| Step 2 | 19.748423 |
| Step 3 | 19.748418 |
After 3 steps the estimate is 19.748418, matching √390 ≈ 19.748418.
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Frequently asked questions
Is 390 a perfect square?
No, 390 is not a perfect square, so its square root is irrational and approximately 19.748418.
What is the square root of 390 in simplest radical form?
√390 = √390 in simplest radical form.