Square Root Calculator › Square root of 442
Square Root of 442
√442 ≈ 21.023796
442 is not a perfect square, so √442 is an irrational number that is approximately 21.023796. In simplified radical form, √442 = √442.
√442 lies between √441 = 21 and √484 = 22.
| Number | 442 |
| Square root (decimal) | 21.023796 |
| Simplified radical | √442 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 442
442 = 2 × 13 × 17. This is what determines the simplified radical: for √442 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √442 is already in simplest radical form as √442.
Estimating √442 by hand
√442 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 442 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.02381 |
| Step 2 | 21.023796 |
| Step 3 | 21.023796 |
After 3 steps the estimate is 21.023796, matching √442 ≈ 21.023796.
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Frequently asked questions
Is 442 a perfect square?
No, 442 is not a perfect square, so its square root is irrational and approximately 21.023796.
What is the square root of 442 in simplest radical form?
√442 = √442 in simplest radical form.