Square Root Calculator › Square root of 557
Square Root of 557
√557 ≈ 23.600847
557 is not a perfect square, so √557 is an irrational number that is approximately 23.600847. In simplified radical form, √557 = √557.
√557 lies between √529 = 23 and √576 = 24.
| Number | 557 |
| Square root (decimal) | 23.600847 |
| Simplified radical | √557 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 557
557 = 557. This is what determines the simplified radical: for √557 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √557 is already in simplest radical form as √557.
Estimating √557 by hand
√557 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 557 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.608696 |
| Step 2 | 23.600849 |
| Step 3 | 23.600847 |
After 3 steps the estimate is 23.600847, matching √557 ≈ 23.600847.
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Frequently asked questions
Is 557 a perfect square?
No, 557 is not a perfect square, so its square root is irrational and approximately 23.600847.
What is the square root of 557 in simplest radical form?
√557 = √557 in simplest radical form.