Square Root Calculator › Square root of 573
Square Root of 573
√573 ≈ 23.937418
573 is not a perfect square, so √573 is an irrational number that is approximately 23.937418. In simplified radical form, √573 = √573.
√573 lies between √529 = 23 and √576 = 24.
| Number | 573 |
| Square root (decimal) | 23.937418 |
| Simplified radical | √573 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 573
573 = 3 × 191. This is what determines the simplified radical: for √573 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √573 is already in simplest radical form as √573.
Estimating √573 by hand
√573 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 573 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.956522 |
| Step 2 | 23.937426 |
| Step 3 | 23.937418 |
After 3 steps the estimate is 23.937418, matching √573 ≈ 23.937418.
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Frequently asked questions
Is 573 a perfect square?
No, 573 is not a perfect square, so its square root is irrational and approximately 23.937418.
What is the square root of 573 in simplest radical form?
√573 = √573 in simplest radical form.