Square Root Calculator › Square root of 386
Square Root of 386
√386 ≈ 19.646883
386 is not a perfect square, so √386 is an irrational number that is approximately 19.646883. In simplified radical form, √386 = √386.
√386 lies between √361 = 19 and √400 = 20.
| Number | 386 |
| Square root (decimal) | 19.646883 |
| Simplified radical | √386 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 386
386 = 2 × 193. This is what determines the simplified radical: for √386 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √386 is already in simplest radical form as √386.
Estimating √386 by hand
√386 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 386 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.657895 |
| Step 2 | 19.646886 |
| Step 3 | 19.646883 |
After 3 steps the estimate is 19.646883, matching √386 ≈ 19.646883.
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Frequently asked questions
Is 386 a perfect square?
No, 386 is not a perfect square, so its square root is irrational and approximately 19.646883.
What is the square root of 386 in simplest radical form?
√386 = √386 in simplest radical form.