Square Root Calculator › Square root of 505
Square Root of 505
√505 ≈ 22.472205
505 is not a perfect square, so √505 is an irrational number that is approximately 22.472205. In simplified radical form, √505 = √505.
√505 lies between √484 = 22 and √529 = 23.
| Number | 505 |
| Square root (decimal) | 22.472205 |
| Simplified radical | √505 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 505
505 = 5 × 101. This is what determines the simplified radical: for √505 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √505 is already in simplest radical form as √505.
Estimating √505 by hand
√505 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 505 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.477273 |
| Step 2 | 22.472206 |
| Step 3 | 22.472205 |
After 3 steps the estimate is 22.472205, matching √505 ≈ 22.472205.
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Frequently asked questions
Is 505 a perfect square?
No, 505 is not a perfect square, so its square root is irrational and approximately 22.472205.
What is the square root of 505 in simplest radical form?
√505 = √505 in simplest radical form.