Square Root Calculator › Square root of 497
Square Root of 497
√497 ≈ 22.293497
497 is not a perfect square, so √497 is an irrational number that is approximately 22.293497. In simplified radical form, √497 = √497.
√497 lies between √484 = 22 and √529 = 23.
| Number | 497 |
| Square root (decimal) | 22.293497 |
| Simplified radical | √497 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 497
497 = 7 × 71. This is what determines the simplified radical: for √497 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √497 is already in simplest radical form as √497.
Estimating √497 by hand
√497 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 497 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.295455 |
| Step 2 | 22.293497 |
| Step 3 | 22.293497 |
After 3 steps the estimate is 22.293497, matching √497 ≈ 22.293497.
Nearby square roots
Frequently asked questions
Is 497 a perfect square?
No, 497 is not a perfect square, so its square root is irrational and approximately 22.293497.
What is the square root of 497 in simplest radical form?
√497 = √497 in simplest radical form.