Square Root Calculator › Square root of 382
Square Root of 382
√382 ≈ 19.54482
382 is not a perfect square, so √382 is an irrational number that is approximately 19.54482. In simplified radical form, √382 = √382.
√382 lies between √361 = 19 and √400 = 20.
| Number | 382 |
| Square root (decimal) | 19.54482 |
| Simplified radical | √382 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 382
382 = 2 × 191. This is what determines the simplified radical: for √382 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √382 is already in simplest radical form as √382.
Estimating √382 by hand
√382 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 382 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.552632 |
| Step 2 | 19.544822 |
| Step 3 | 19.54482 |
After 3 steps the estimate is 19.54482, matching √382 ≈ 19.54482.
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Frequently asked questions
Is 382 a perfect square?
No, 382 is not a perfect square, so its square root is irrational and approximately 19.54482.
What is the square root of 382 in simplest radical form?
√382 = √382 in simplest radical form.