Square Root Calculator › Square root of 492
Square Root of 492
√492 ≈ 22.181073
492 is not a perfect square, so √492 is an irrational number that is approximately 22.181073. In simplified radical form, √492 = 2√123.
√492 lies between √484 = 22 and √529 = 23.
| Number | 492 |
| Square root (decimal) | 22.181073 |
| Simplified radical | 2√123 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 492
492 = 2^2 × 3 × 41. This is what determines the simplified radical: for √492 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √492 = 2√123.
Estimating √492 by hand
√492 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 492 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.181818 |
| Step 2 | 22.181073 |
| Step 3 | 22.181073 |
After 3 steps the estimate is 22.181073, matching √492 ≈ 22.181073.
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Frequently asked questions
Is 492 a perfect square?
No, 492 is not a perfect square, so its square root is irrational and approximately 22.181073.
What is the square root of 492 in simplest radical form?
√492 = 2√123 in simplest radical form.