Square Root Calculator › Square root of 560
Square Root of 560
√560 ≈ 23.664319
560 is not a perfect square, so √560 is an irrational number that is approximately 23.664319. In simplified radical form, √560 = 4√35.
√560 lies between √529 = 23 and √576 = 24.
| Number | 560 |
| Square root (decimal) | 23.664319 |
| Simplified radical | 4√35 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 560
560 = 2^4 × 5 × 7. This is what determines the simplified radical: for √560 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √560 = 4√35.
Estimating √560 by hand
√560 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 560 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.673913 |
| Step 2 | 23.664321 |
| Step 3 | 23.664319 |
After 3 steps the estimate is 23.664319, matching √560 ≈ 23.664319.
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Frequently asked questions
Is 560 a perfect square?
No, 560 is not a perfect square, so its square root is irrational and approximately 23.664319.
What is the square root of 560 in simplest radical form?
√560 = 4√35 in simplest radical form.