Square Root Calculator › Square root of 363
Square Root of 363
√363 ≈ 19.052559
363 is not a perfect square, so √363 is an irrational number that is approximately 19.052559. In simplified radical form, √363 = 11√3.
√363 lies between √361 = 19 and √400 = 20.
| Number | 363 |
| Square root (decimal) | 19.052559 |
| Simplified radical | 11√3 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 363
363 = 3 × 11^2. This is what determines the simplified radical: for √363 you pull out one copy of any prime that appears twice.
Here the paired factor 11 comes out from under the root, leaving √363 = 11√3.
Estimating √363 by hand
√363 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 363 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.052632 |
| Step 2 | 19.052559 |
| Step 3 | 19.052559 |
After 3 steps the estimate is 19.052559, matching √363 ≈ 19.052559.
Nearby square roots
Frequently asked questions
Is 363 a perfect square?
No, 363 is not a perfect square, so its square root is irrational and approximately 19.052559.
What is the square root of 363 in simplest radical form?
√363 = 11√3 in simplest radical form.