Square Root Calculator › Square root of 531
Square Root of 531
√531 ≈ 23.043437
531 is not a perfect square, so √531 is an irrational number that is approximately 23.043437. In simplified radical form, √531 = 3√59.
√531 lies between √529 = 23 and √576 = 24.
| Number | 531 |
| Square root (decimal) | 23.043437 |
| Simplified radical | 3√59 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 531
531 = 3^2 × 59. This is what determines the simplified radical: for √531 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √531 = 3√59.
Estimating √531 by hand
√531 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 531 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.043478 |
| Step 2 | 23.043437 |
| Step 3 | 23.043437 |
After 3 steps the estimate is 23.043437, matching √531 ≈ 23.043437.
Nearby square roots
Frequently asked questions
Is 531 a perfect square?
No, 531 is not a perfect square, so its square root is irrational and approximately 23.043437.
What is the square root of 531 in simplest radical form?
√531 = 3√59 in simplest radical form.