Square Root Calculator › Square root of 528
Square Root of 528
√528 ≈ 22.978251
528 is not a perfect square, so √528 is an irrational number that is approximately 22.978251. In simplified radical form, √528 = 4√33.
√528 lies between √484 = 22 and √529 = 23.
| Number | 528 |
| Square root (decimal) | 22.978251 |
| Simplified radical | 4√33 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 528
528 = 2^4 × 3 × 11. This is what determines the simplified radical: for √528 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √528 = 4√33.
Estimating √528 by hand
√528 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 528 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 23 |
| Step 2 | 22.978261 |
| Step 3 | 22.978251 |
After 3 steps the estimate is 22.978251, matching √528 ≈ 22.978251.
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Frequently asked questions
Is 528 a perfect square?
No, 528 is not a perfect square, so its square root is irrational and approximately 22.978251.
What is the square root of 528 in simplest radical form?
√528 = 4√33 in simplest radical form.