Square Root Calculator › Square root of 568
Square Root of 568
√568 ≈ 23.832751
568 is not a perfect square, so √568 is an irrational number that is approximately 23.832751. In simplified radical form, √568 = 2√142.
√568 lies between √529 = 23 and √576 = 24.
| Number | 568 |
| Square root (decimal) | 23.832751 |
| Simplified radical | 2√142 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 568
568 = 2^3 × 71. This is what determines the simplified radical: for √568 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √568 = 2√142.
Estimating √568 by hand
√568 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 568 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.847826 |
| Step 2 | 23.832755 |
| Step 3 | 23.832751 |
After 3 steps the estimate is 23.832751, matching √568 ≈ 23.832751.
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Frequently asked questions
Is 568 a perfect square?
No, 568 is not a perfect square, so its square root is irrational and approximately 23.832751.
What is the square root of 568 in simplest radical form?
√568 = 2√142 in simplest radical form.