Square Root Calculator › Square root of 449
Square Root of 449
√449 ≈ 21.18962
449 is not a perfect square, so √449 is an irrational number that is approximately 21.18962. In simplified radical form, √449 = √449.
√449 lies between √441 = 21 and √484 = 22.
| Number | 449 |
| Square root (decimal) | 21.18962 |
| Simplified radical | √449 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 449
449 = 449. This is what determines the simplified radical: for √449 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √449 is already in simplest radical form as √449.
Estimating √449 by hand
√449 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 449 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.190476 |
| Step 2 | 21.18962 |
| Step 3 | 21.18962 |
After 3 steps the estimate is 21.18962, matching √449 ≈ 21.18962.
Nearby square roots
Frequently asked questions
Is 449 a perfect square?
No, 449 is not a perfect square, so its square root is irrational and approximately 21.18962.
What is the square root of 449 in simplest radical form?
√449 = √449 in simplest radical form.