Square Root Calculator › Square root of 496
Square Root of 496
√496 ≈ 22.271057
496 is not a perfect square, so √496 is an irrational number that is approximately 22.271057. In simplified radical form, √496 = 4√31.
√496 lies between √484 = 22 and √529 = 23.
| Number | 496 |
| Square root (decimal) | 22.271057 |
| Simplified radical | 4√31 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 496
496 = 2^4 × 31. This is what determines the simplified radical: for √496 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √496 = 4√31.
Estimating √496 by hand
√496 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 496 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.272727 |
| Step 2 | 22.271058 |
| Step 3 | 22.271057 |
After 3 steps the estimate is 22.271057, matching √496 ≈ 22.271057.
Nearby square roots
Frequently asked questions
Is 496 a perfect square?
No, 496 is not a perfect square, so its square root is irrational and approximately 22.271057.
What is the square root of 496 in simplest radical form?
√496 = 4√31 in simplest radical form.