Square Root Calculator › Square root of 552
Square Root of 552
√552 ≈ 23.49468
552 is not a perfect square, so √552 is an irrational number that is approximately 23.49468. In simplified radical form, √552 = 2√138.
√552 lies between √529 = 23 and √576 = 24.
| Number | 552 |
| Square root (decimal) | 23.49468 |
| Simplified radical | 2√138 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 552
552 = 2^3 × 3 × 23. This is what determines the simplified radical: for √552 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √552 = 2√138.
Estimating √552 by hand
√552 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 552 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.5 |
| Step 2 | 23.494681 |
| Step 3 | 23.49468 |
After 3 steps the estimate is 23.49468, matching √552 ≈ 23.49468.
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Frequently asked questions
Is 552 a perfect square?
No, 552 is not a perfect square, so its square root is irrational and approximately 23.49468.
What is the square root of 552 in simplest radical form?
√552 = 2√138 in simplest radical form.