Square Root Calculator › Square root of 443
Square Root of 443
√443 ≈ 21.047565
443 is not a perfect square, so √443 is an irrational number that is approximately 21.047565. In simplified radical form, √443 = √443.
√443 lies between √441 = 21 and √484 = 22.
| Number | 443 |
| Square root (decimal) | 21.047565 |
| Simplified radical | √443 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 443
443 = 443. This is what determines the simplified radical: for √443 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √443 is already in simplest radical form as √443.
Estimating √443 by hand
√443 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 443 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.047619 |
| Step 2 | 21.047565 |
| Step 3 | 21.047565 |
After 3 steps the estimate is 21.047565, matching √443 ≈ 21.047565.
Nearby square roots
Frequently asked questions
Is 443 a perfect square?
No, 443 is not a perfect square, so its square root is irrational and approximately 21.047565.
What is the square root of 443 in simplest radical form?
√443 = √443 in simplest radical form.