Square Root Calculator › Square root of 561
Square Root of 561
√561 ≈ 23.685439
561 is not a perfect square, so √561 is an irrational number that is approximately 23.685439. In simplified radical form, √561 = √561.
√561 lies between √529 = 23 and √576 = 24.
| Number | 561 |
| Square root (decimal) | 23.685439 |
| Simplified radical | √561 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 561
561 = 3 × 11 × 17. This is what determines the simplified radical: for √561 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √561 is already in simplest radical form as √561.
Estimating √561 by hand
√561 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 561 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.695652 |
| Step 2 | 23.685441 |
| Step 3 | 23.685439 |
After 3 steps the estimate is 23.685439, matching √561 ≈ 23.685439.
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Frequently asked questions
Is 561 a perfect square?
No, 561 is not a perfect square, so its square root is irrational and approximately 23.685439.
What is the square root of 561 in simplest radical form?
√561 = √561 in simplest radical form.