Square Root Calculator › Square root of 369
Square Root of 369
√369 ≈ 19.209373
369 is not a perfect square, so √369 is an irrational number that is approximately 19.209373. In simplified radical form, √369 = 3√41.
√369 lies between √361 = 19 and √400 = 20.
| Number | 369 |
| Square root (decimal) | 19.209373 |
| Simplified radical | 3√41 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 369
369 = 3^2 × 41. This is what determines the simplified radical: for √369 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √369 = 3√41.
Estimating √369 by hand
√369 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 369 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.210526 |
| Step 2 | 19.209373 |
| Step 3 | 19.209373 |
After 3 steps the estimate is 19.209373, matching √369 ≈ 19.209373.
Nearby square roots
Frequently asked questions
Is 369 a perfect square?
No, 369 is not a perfect square, so its square root is irrational and approximately 19.209373.
What is the square root of 369 in simplest radical form?
√369 = 3√41 in simplest radical form.