Square Root Calculator › Square root of 532
Square Root of 532
√532 ≈ 23.065125
532 is not a perfect square, so √532 is an irrational number that is approximately 23.065125. In simplified radical form, √532 = 2√133.
√532 lies between √529 = 23 and √576 = 24.
| Number | 532 |
| Square root (decimal) | 23.065125 |
| Simplified radical | 2√133 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 532
532 = 2^2 × 7 × 19. This is what determines the simplified radical: for √532 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √532 = 2√133.
Estimating √532 by hand
√532 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 532 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.065217 |
| Step 2 | 23.065125 |
| Step 3 | 23.065125 |
After 3 steps the estimate is 23.065125, matching √532 ≈ 23.065125.
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Frequently asked questions
Is 532 a perfect square?
No, 532 is not a perfect square, so its square root is irrational and approximately 23.065125.
What is the square root of 532 in simplest radical form?
√532 = 2√133 in simplest radical form.