Square Root Calculator › Square root of 549
Square Root of 549
√549 ≈ 23.430749
549 is not a perfect square, so √549 is an irrational number that is approximately 23.430749. In simplified radical form, √549 = 3√61.
√549 lies between √529 = 23 and √576 = 24.
| Number | 549 |
| Square root (decimal) | 23.430749 |
| Simplified radical | 3√61 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 549
549 = 3^2 × 61. This is what determines the simplified radical: for √549 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √549 = 3√61.
Estimating √549 by hand
√549 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 549 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.434783 |
| Step 2 | 23.430749 |
| Step 3 | 23.430749 |
After 3 steps the estimate is 23.430749, matching √549 ≈ 23.430749.
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Frequently asked questions
Is 549 a perfect square?
No, 549 is not a perfect square, so its square root is irrational and approximately 23.430749.
What is the square root of 549 in simplest radical form?
√549 = 3√61 in simplest radical form.