Square Root Calculator › Square root of 444
Square Root of 444
√444 ≈ 21.071308
444 is not a perfect square, so √444 is an irrational number that is approximately 21.071308. In simplified radical form, √444 = 2√111.
√444 lies between √441 = 21 and √484 = 22.
| Number | 444 |
| Square root (decimal) | 21.071308 |
| Simplified radical | 2√111 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 444
444 = 2^2 × 3 × 37. This is what determines the simplified radical: for √444 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √444 = 2√111.
Estimating √444 by hand
√444 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 444 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.071429 |
| Step 2 | 21.071308 |
| Step 3 | 21.071308 |
After 3 steps the estimate is 21.071308, matching √444 ≈ 21.071308.
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Frequently asked questions
Is 444 a perfect square?
No, 444 is not a perfect square, so its square root is irrational and approximately 21.071308.
What is the square root of 444 in simplest radical form?
√444 = 2√111 in simplest radical form.