Square Root Calculator › Square root of 567
Square Root of 567
√567 ≈ 23.811762
567 is not a perfect square, so √567 is an irrational number that is approximately 23.811762. In simplified radical form, √567 = 9√7.
√567 lies between √529 = 23 and √576 = 24.
| Number | 567 |
| Square root (decimal) | 23.811762 |
| Simplified radical | 9√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 567
567 = 3^4 × 7. This is what determines the simplified radical: for √567 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √567 = 9√7.
Estimating √567 by hand
√567 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 567 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.826087 |
| Step 2 | 23.811766 |
| Step 3 | 23.811762 |
After 3 steps the estimate is 23.811762, matching √567 ≈ 23.811762.
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Frequently asked questions
Is 567 a perfect square?
No, 567 is not a perfect square, so its square root is irrational and approximately 23.811762.
What is the square root of 567 in simplest radical form?
√567 = 9√7 in simplest radical form.