Square Root Calculator › Square root of 389
Square Root of 389
√389 ≈ 19.723083
389 is not a perfect square, so √389 is an irrational number that is approximately 19.723083. In simplified radical form, √389 = √389.
√389 lies between √361 = 19 and √400 = 20.
| Number | 389 |
| Square root (decimal) | 19.723083 |
| Simplified radical | √389 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 389
389 = 389. This is what determines the simplified radical: for √389 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √389 is already in simplest radical form as √389.
Estimating √389 by hand
√389 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 389 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.736842 |
| Step 2 | 19.723088 |
| Step 3 | 19.723083 |
After 3 steps the estimate is 19.723083, matching √389 ≈ 19.723083.
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Frequently asked questions
Is 389 a perfect square?
No, 389 is not a perfect square, so its square root is irrational and approximately 19.723083.
What is the square root of 389 in simplest radical form?
√389 = √389 in simplest radical form.