Square Root Calculator › Square root of 537
Square Root of 537
√537 ≈ 23.17326
537 is not a perfect square, so √537 is an irrational number that is approximately 23.17326. In simplified radical form, √537 = √537.
√537 lies between √529 = 23 and √576 = 24.
| Number | 537 |
| Square root (decimal) | 23.17326 |
| Simplified radical | √537 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 537
537 = 3 × 179. This is what determines the simplified radical: for √537 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √537 is already in simplest radical form as √537.
Estimating √537 by hand
√537 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 537 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.173913 |
| Step 2 | 23.17326 |
| Step 3 | 23.17326 |
After 3 steps the estimate is 23.17326, matching √537 ≈ 23.17326.
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Frequently asked questions
Is 537 a perfect square?
No, 537 is not a perfect square, so its square root is irrational and approximately 23.17326.
What is the square root of 537 in simplest radical form?
√537 = √537 in simplest radical form.