Square Root Calculator › Square root of 580
Square Root of 580
√580 ≈ 24.083189
580 is not a perfect square, so √580 is an irrational number that is approximately 24.083189. In simplified radical form, √580 = 2√145.
√580 lies between √576 = 24 and √625 = 25.
| Number | 580 |
| Square root (decimal) | 24.083189 |
| Simplified radical | 2√145 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 580
580 = 2^2 × 5 × 29. This is what determines the simplified radical: for √580 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √580 = 2√145.
Estimating √580 by hand
√580 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 580 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.083333 |
| Step 2 | 24.083189 |
| Step 3 | 24.083189 |
After 3 steps the estimate is 24.083189, matching √580 ≈ 24.083189.
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Frequently asked questions
Is 580 a perfect square?
No, 580 is not a perfect square, so its square root is irrational and approximately 24.083189.
What is the square root of 580 in simplest radical form?
√580 = 2√145 in simplest radical form.