Square Root Calculator › Square root of 481
Square Root of 481
√481 ≈ 21.931712
481 is not a perfect square, so √481 is an irrational number that is approximately 21.931712. In simplified radical form, √481 = √481.
√481 lies between √441 = 21 and √484 = 22.
| Number | 481 |
| Square root (decimal) | 21.931712 |
| Simplified radical | √481 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 481
481 = 13 × 37. This is what determines the simplified radical: for √481 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √481 is already in simplest radical form as √481.
Estimating √481 by hand
√481 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 481 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.952381 |
| Step 2 | 21.931722 |
| Step 3 | 21.931712 |
After 3 steps the estimate is 21.931712, matching √481 ≈ 21.931712.
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Frequently asked questions
Is 481 a perfect square?
No, 481 is not a perfect square, so its square root is irrational and approximately 21.931712.
What is the square root of 481 in simplest radical form?
√481 = √481 in simplest radical form.