Square Root Calculator › Square root of 504
Square Root of 504
√504 ≈ 22.449944
504 is not a perfect square, so √504 is an irrational number that is approximately 22.449944. In simplified radical form, √504 = 6√14.
√504 lies between √484 = 22 and √529 = 23.
| Number | 504 |
| Square root (decimal) | 22.449944 |
| Simplified radical | 6√14 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 504
504 = 2^3 × 3^2 × 7. This is what determines the simplified radical: for √504 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √504 = 6√14.
Estimating √504 by hand
√504 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 504 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.454545 |
| Step 2 | 22.449945 |
| Step 3 | 22.449944 |
After 3 steps the estimate is 22.449944, matching √504 ≈ 22.449944.
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Frequently asked questions
Is 504 a perfect square?
No, 504 is not a perfect square, so its square root is irrational and approximately 22.449944.
What is the square root of 504 in simplest radical form?
√504 = 6√14 in simplest radical form.