Square Root Calculator › Square root of 553
Square Root of 553
√553 ≈ 23.515952
553 is not a perfect square, so √553 is an irrational number that is approximately 23.515952. In simplified radical form, √553 = √553.
√553 lies between √529 = 23 and √576 = 24.
| Number | 553 |
| Square root (decimal) | 23.515952 |
| Simplified radical | √553 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 553
553 = 7 × 79. This is what determines the simplified radical: for √553 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √553 is already in simplest radical form as √553.
Estimating √553 by hand
√553 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 553 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.521739 |
| Step 2 | 23.515953 |
| Step 3 | 23.515952 |
After 3 steps the estimate is 23.515952, matching √553 ≈ 23.515952.
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Frequently asked questions
Is 553 a perfect square?
No, 553 is not a perfect square, so its square root is irrational and approximately 23.515952.
What is the square root of 553 in simplest radical form?
√553 = √553 in simplest radical form.