Square Root Calculator › Square root of 558
Square Root of 558
√558 ≈ 23.622024
558 is not a perfect square, so √558 is an irrational number that is approximately 23.622024. In simplified radical form, √558 = 3√62.
√558 lies between √529 = 23 and √576 = 24.
| Number | 558 |
| Square root (decimal) | 23.622024 |
| Simplified radical | 3√62 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 558
558 = 2 × 3^2 × 31. This is what determines the simplified radical: for √558 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √558 = 3√62.
Estimating √558 by hand
√558 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 558 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.630435 |
| Step 2 | 23.622025 |
| Step 3 | 23.622024 |
After 3 steps the estimate is 23.622024, matching √558 ≈ 23.622024.
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Frequently asked questions
Is 558 a perfect square?
No, 558 is not a perfect square, so its square root is irrational and approximately 23.622024.
What is the square root of 558 in simplest radical form?
√558 = 3√62 in simplest radical form.