Square Root Calculator › Square root of 574
Square Root of 574
√574 ≈ 23.958297
574 is not a perfect square, so √574 is an irrational number that is approximately 23.958297. In simplified radical form, √574 = √574.
√574 lies between √529 = 23 and √576 = 24.
| Number | 574 |
| Square root (decimal) | 23.958297 |
| Simplified radical | √574 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 574
574 = 2 × 7 × 41. This is what determines the simplified radical: for √574 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √574 is already in simplest radical form as √574.
Estimating √574 by hand
√574 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 574 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.978261 |
| Step 2 | 23.958305 |
| Step 3 | 23.958297 |
After 3 steps the estimate is 23.958297, matching √574 ≈ 23.958297.
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Frequently asked questions
Is 574 a perfect square?
No, 574 is not a perfect square, so its square root is irrational and approximately 23.958297.
What is the square root of 574 in simplest radical form?
√574 = √574 in simplest radical form.