Square Root Calculator › Square root of 596
Square Root of 596
√596 ≈ 24.413111
596 is not a perfect square, so √596 is an irrational number that is approximately 24.413111. In simplified radical form, √596 = 2√149.
√596 lies between √576 = 24 and √625 = 25.
| Number | 596 |
| Square root (decimal) | 24.413111 |
| Simplified radical | 2√149 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 596
596 = 2^2 × 149. This is what determines the simplified radical: for √596 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √596 = 2√149.
Estimating √596 by hand
√596 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 596 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.416667 |
| Step 2 | 24.413111 |
| Step 3 | 24.413111 |
After 3 steps the estimate is 24.413111, matching √596 ≈ 24.413111.
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Frequently asked questions
Is 596 a perfect square?
No, 596 is not a perfect square, so its square root is irrational and approximately 24.413111.
What is the square root of 596 in simplest radical form?
√596 = 2√149 in simplest radical form.