Square Root Calculator › Square root of 485
Square Root of 485
√485 ≈ 22.022716
485 is not a perfect square, so √485 is an irrational number that is approximately 22.022716. In simplified radical form, √485 = √485.
√485 lies between √484 = 22 and √529 = 23.
| Number | 485 |
| Square root (decimal) | 22.022716 |
| Simplified radical | √485 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 485
485 = 5 × 97. This is what determines the simplified radical: for √485 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √485 is already in simplest radical form as √485.
Estimating √485 by hand
√485 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 485 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.022727 |
| Step 2 | 22.022716 |
| Step 3 | 22.022716 |
After 3 steps the estimate is 22.022716, matching √485 ≈ 22.022716.
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Frequently asked questions
Is 485 a perfect square?
No, 485 is not a perfect square, so its square root is irrational and approximately 22.022716.
What is the square root of 485 in simplest radical form?
√485 = √485 in simplest radical form.