Square Root Calculator › Square root of 563
Square Root of 563
√563 ≈ 23.727621
563 is not a perfect square, so √563 is an irrational number that is approximately 23.727621. In simplified radical form, √563 = √563.
√563 lies between √529 = 23 and √576 = 24.
| Number | 563 |
| Square root (decimal) | 23.727621 |
| Simplified radical | √563 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 563
563 = 563. This is what determines the simplified radical: for √563 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √563 is already in simplest radical form as √563.
Estimating √563 by hand
√563 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 563 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.73913 |
| Step 2 | 23.727624 |
| Step 3 | 23.727621 |
After 3 steps the estimate is 23.727621, matching √563 ≈ 23.727621.
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Frequently asked questions
Is 563 a perfect square?
No, 563 is not a perfect square, so its square root is irrational and approximately 23.727621.
What is the square root of 563 in simplest radical form?
√563 = √563 in simplest radical form.