Square Root Calculator › Square root of 533
Square Root of 533
√533 ≈ 23.086793
533 is not a perfect square, so √533 is an irrational number that is approximately 23.086793. In simplified radical form, √533 = √533.
√533 lies between √529 = 23 and √576 = 24.
| Number | 533 |
| Square root (decimal) | 23.086793 |
| Simplified radical | √533 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 533
533 = 13 × 41. This is what determines the simplified radical: for √533 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √533 is already in simplest radical form as √533.
Estimating √533 by hand
√533 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 533 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.086957 |
| Step 2 | 23.086793 |
| Step 3 | 23.086793 |
After 3 steps the estimate is 23.086793, matching √533 ≈ 23.086793.
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Frequently asked questions
Is 533 a perfect square?
No, 533 is not a perfect square, so its square root is irrational and approximately 23.086793.
What is the square root of 533 in simplest radical form?
√533 = √533 in simplest radical form.