Square Root Calculator › Square root of 502
Square Root of 502
√502 ≈ 22.405357
502 is not a perfect square, so √502 is an irrational number that is approximately 22.405357. In simplified radical form, √502 = √502.
√502 lies between √484 = 22 and √529 = 23.
| Number | 502 |
| Square root (decimal) | 22.405357 |
| Simplified radical | √502 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 502
502 = 2 × 251. This is what determines the simplified radical: for √502 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √502 is already in simplest radical form as √502.
Estimating √502 by hand
√502 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 502 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.409091 |
| Step 2 | 22.405357 |
| Step 3 | 22.405357 |
After 3 steps the estimate is 22.405357, matching √502 ≈ 22.405357.
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Frequently asked questions
Is 502 a perfect square?
No, 502 is not a perfect square, so its square root is irrational and approximately 22.405357.
What is the square root of 502 in simplest radical form?
√502 = √502 in simplest radical form.