Square Root Calculator › Square root of 482
Square Root of 482
√482 ≈ 21.954498
482 is not a perfect square, so √482 is an irrational number that is approximately 21.954498. In simplified radical form, √482 = √482.
√482 lies between √441 = 21 and √484 = 22.
| Number | 482 |
| Square root (decimal) | 21.954498 |
| Simplified radical | √482 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 482
482 = 2 × 241. This is what determines the simplified radical: for √482 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √482 is already in simplest radical form as √482.
Estimating √482 by hand
√482 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 482 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.97619 |
| Step 2 | 21.954509 |
| Step 3 | 21.954498 |
After 3 steps the estimate is 21.954498, matching √482 ≈ 21.954498.
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Frequently asked questions
Is 482 a perfect square?
No, 482 is not a perfect square, so its square root is irrational and approximately 21.954498.
What is the square root of 482 in simplest radical form?
√482 = √482 in simplest radical form.