Square Root Calculator › Square root of 446
Square Root of 446
√446 ≈ 21.118712
446 is not a perfect square, so √446 is an irrational number that is approximately 21.118712. In simplified radical form, √446 = √446.
√446 lies between √441 = 21 and √484 = 22.
| Number | 446 |
| Square root (decimal) | 21.118712 |
| Simplified radical | √446 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 446
446 = 2 × 223. This is what determines the simplified radical: for √446 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √446 is already in simplest radical form as √446.
Estimating √446 by hand
√446 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 446 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.119048 |
| Step 2 | 21.118712 |
| Step 3 | 21.118712 |
After 3 steps the estimate is 21.118712, matching √446 ≈ 21.118712.
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Frequently asked questions
Is 446 a perfect square?
No, 446 is not a perfect square, so its square root is irrational and approximately 21.118712.
What is the square root of 446 in simplest radical form?
√446 = √446 in simplest radical form.