Square Root Calculator › Square root of 380
Square Root of 380
√380 ≈ 19.493589
380 is not a perfect square, so √380 is an irrational number that is approximately 19.493589. In simplified radical form, √380 = 2√95.
√380 lies between √361 = 19 and √400 = 20.
| Number | 380 |
| Square root (decimal) | 19.493589 |
| Simplified radical | 2√95 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 380
380 = 2^2 × 5 × 19. This is what determines the simplified radical: for √380 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √380 = 2√95.
Estimating √380 by hand
√380 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 380 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.5 |
| Step 2 | 19.49359 |
| Step 3 | 19.493589 |
After 3 steps the estimate is 19.493589, matching √380 ≈ 19.493589.
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Frequently asked questions
Is 380 a perfect square?
No, 380 is not a perfect square, so its square root is irrational and approximately 19.493589.
What is the square root of 380 in simplest radical form?
√380 = 2√95 in simplest radical form.