Square Root Calculator › Square root of 494
Square Root of 494
√494 ≈ 22.226111
494 is not a perfect square, so √494 is an irrational number that is approximately 22.226111. In simplified radical form, √494 = √494.
√494 lies between √484 = 22 and √529 = 23.
| Number | 494 |
| Square root (decimal) | 22.226111 |
| Simplified radical | √494 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 494
494 = 2 × 13 × 19. This is what determines the simplified radical: for √494 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √494 is already in simplest radical form as √494.
Estimating √494 by hand
√494 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 494 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.227273 |
| Step 2 | 22.226111 |
| Step 3 | 22.226111 |
After 3 steps the estimate is 22.226111, matching √494 ≈ 22.226111.
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Frequently asked questions
Is 494 a perfect square?
No, 494 is not a perfect square, so its square root is irrational and approximately 22.226111.
What is the square root of 494 in simplest radical form?
√494 = √494 in simplest radical form.