Square Root Calculator › Square root of 530
Square Root of 530
√530 ≈ 23.021729
530 is not a perfect square, so √530 is an irrational number that is approximately 23.021729. In simplified radical form, √530 = √530.
√530 lies between √529 = 23 and √576 = 24.
| Number | 530 |
| Square root (decimal) | 23.021729 |
| Simplified radical | √530 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 530
530 = 2 × 5 × 53. This is what determines the simplified radical: for √530 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √530 is already in simplest radical form as √530.
Estimating √530 by hand
√530 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 530 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.021739 |
| Step 2 | 23.021729 |
| Step 3 | 23.021729 |
After 3 steps the estimate is 23.021729, matching √530 ≈ 23.021729.
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Frequently asked questions
Is 530 a perfect square?
No, 530 is not a perfect square, so its square root is irrational and approximately 23.021729.
What is the square root of 530 in simplest radical form?
√530 = √530 in simplest radical form.