Square Root Calculator › Square root of 385
Square Root of 385
√385 ≈ 19.621417
385 is not a perfect square, so √385 is an irrational number that is approximately 19.621417. In simplified radical form, √385 = √385.
√385 lies between √361 = 19 and √400 = 20.
| Number | 385 |
| Square root (decimal) | 19.621417 |
| Simplified radical | √385 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 385
385 = 5 × 7 × 11. This is what determines the simplified radical: for √385 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √385 is already in simplest radical form as √385.
Estimating √385 by hand
√385 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 385 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.631579 |
| Step 2 | 19.62142 |
| Step 3 | 19.621417 |
After 3 steps the estimate is 19.621417, matching √385 ≈ 19.621417.
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Frequently asked questions
Is 385 a perfect square?
No, 385 is not a perfect square, so its square root is irrational and approximately 19.621417.
What is the square root of 385 in simplest radical form?
√385 = √385 in simplest radical form.