Square Root Calculator › Square root of 581
Square Root of 581
√581 ≈ 24.103942
581 is not a perfect square, so √581 is an irrational number that is approximately 24.103942. In simplified radical form, √581 = √581.
√581 lies between √576 = 24 and √625 = 25.
| Number | 581 |
| Square root (decimal) | 24.103942 |
| Simplified radical | √581 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 581
581 = 7 × 83. This is what determines the simplified radical: for √581 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √581 is already in simplest radical form as √581.
Estimating √581 by hand
√581 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 581 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.104167 |
| Step 2 | 24.103942 |
| Step 3 | 24.103942 |
After 3 steps the estimate is 24.103942, matching √581 ≈ 24.103942.
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Frequently asked questions
Is 581 a perfect square?
No, 581 is not a perfect square, so its square root is irrational and approximately 24.103942.
What is the square root of 581 in simplest radical form?
√581 = √581 in simplest radical form.