Square Root Calculator › Square root of 572
Square Root of 572
√572 ≈ 23.916521
572 is not a perfect square, so √572 is an irrational number that is approximately 23.916521. In simplified radical form, √572 = 2√143.
√572 lies between √529 = 23 and √576 = 24.
| Number | 572 |
| Square root (decimal) | 23.916521 |
| Simplified radical | 2√143 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 572
572 = 2^2 × 11 × 13. This is what determines the simplified radical: for √572 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √572 = 2√143.
Estimating √572 by hand
√572 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 572 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.934783 |
| Step 2 | 23.916528 |
| Step 3 | 23.916521 |
After 3 steps the estimate is 23.916521, matching √572 ≈ 23.916521.
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Frequently asked questions
Is 572 a perfect square?
No, 572 is not a perfect square, so its square root is irrational and approximately 23.916521.
What is the square root of 572 in simplest radical form?
√572 = 2√143 in simplest radical form.