Square Root Calculator › Square root of 539
Square Root of 539
√539 ≈ 23.216374
539 is not a perfect square, so √539 is an irrational number that is approximately 23.216374. In simplified radical form, √539 = 7√11.
√539 lies between √529 = 23 and √576 = 24.
| Number | 539 |
| Square root (decimal) | 23.216374 |
| Simplified radical | 7√11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 539
539 = 7^2 × 11. This is what determines the simplified radical: for √539 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √539 = 7√11.
Estimating √539 by hand
√539 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 539 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.217391 |
| Step 2 | 23.216374 |
| Step 3 | 23.216374 |
After 3 steps the estimate is 23.216374, matching √539 ≈ 23.216374.
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Frequently asked questions
Is 539 a perfect square?
No, 539 is not a perfect square, so its square root is irrational and approximately 23.216374.
What is the square root of 539 in simplest radical form?
√539 = 7√11 in simplest radical form.