Square Root Calculator › Square root of 566
Square Root of 566
√566 ≈ 23.790755
566 is not a perfect square, so √566 is an irrational number that is approximately 23.790755. In simplified radical form, √566 = √566.
√566 lies between √529 = 23 and √576 = 24.
| Number | 566 |
| Square root (decimal) | 23.790755 |
| Simplified radical | √566 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 566
566 = 2 × 283. This is what determines the simplified radical: for √566 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √566 is already in simplest radical form as √566.
Estimating √566 by hand
√566 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 566 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.804348 |
| Step 2 | 23.790758 |
| Step 3 | 23.790755 |
After 3 steps the estimate is 23.790755, matching √566 ≈ 23.790755.
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Frequently asked questions
Is 566 a perfect square?
No, 566 is not a perfect square, so its square root is irrational and approximately 23.790755.
What is the square root of 566 in simplest radical form?
√566 = √566 in simplest radical form.