Square Root Calculator › Square root of 590
Square Root of 590
√590 ≈ 24.289916
590 is not a perfect square, so √590 is an irrational number that is approximately 24.289916. In simplified radical form, √590 = √590.
√590 lies between √576 = 24 and √625 = 25.
| Number | 590 |
| Square root (decimal) | 24.289916 |
| Simplified radical | √590 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 590
590 = 2 × 5 × 59. This is what determines the simplified radical: for √590 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √590 is already in simplest radical form as √590.
Estimating √590 by hand
√590 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 590 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.291667 |
| Step 2 | 24.289916 |
| Step 3 | 24.289916 |
After 3 steps the estimate is 24.289916, matching √590 ≈ 24.289916.
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Frequently asked questions
Is 590 a perfect square?
No, 590 is not a perfect square, so its square root is irrational and approximately 24.289916.
What is the square root of 590 in simplest radical form?
√590 = √590 in simplest radical form.