Square Root Calculator › Square root of 498
Square Root of 498
√498 ≈ 22.315914
498 is not a perfect square, so √498 is an irrational number that is approximately 22.315914. In simplified radical form, √498 = √498.
√498 lies between √484 = 22 and √529 = 23.
| Number | 498 |
| Square root (decimal) | 22.315914 |
| Simplified radical | √498 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 498
498 = 2 × 3 × 83. This is what determines the simplified radical: for √498 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √498 is already in simplest radical form as √498.
Estimating √498 by hand
√498 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 498 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.318182 |
| Step 2 | 22.315914 |
| Step 3 | 22.315914 |
After 3 steps the estimate is 22.315914, matching √498 ≈ 22.315914.
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Frequently asked questions
Is 498 a perfect square?
No, 498 is not a perfect square, so its square root is irrational and approximately 22.315914.
What is the square root of 498 in simplest radical form?
√498 = √498 in simplest radical form.