Square Root Calculator › Square root of 394
Square Root of 394
√394 ≈ 19.849433
394 is not a perfect square, so √394 is an irrational number that is approximately 19.849433. In simplified radical form, √394 = √394.
√394 lies between √361 = 19 and √400 = 20.
| Number | 394 |
| Square root (decimal) | 19.849433 |
| Simplified radical | √394 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 394
394 = 2 × 197. This is what determines the simplified radical: for √394 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √394 is already in simplest radical form as √394.
Estimating √394 by hand
√394 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 394 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.868421 |
| Step 2 | 19.849442 |
| Step 3 | 19.849433 |
After 3 steps the estimate is 19.849433, matching √394 ≈ 19.849433.
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Frequently asked questions
Is 394 a perfect square?
No, 394 is not a perfect square, so its square root is irrational and approximately 19.849433.
What is the square root of 394 in simplest radical form?
√394 = √394 in simplest radical form.