Square Root Calculator › Square root of 544
Square Root of 544
√544 ≈ 23.323808
544 is not a perfect square, so √544 is an irrational number that is approximately 23.323808. In simplified radical form, √544 = 4√34.
√544 lies between √529 = 23 and √576 = 24.
| Number | 544 |
| Square root (decimal) | 23.323808 |
| Simplified radical | 4√34 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 544
544 = 2^5 × 17. This is what determines the simplified radical: for √544 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √544 = 4√34.
Estimating √544 by hand
√544 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 544 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.326087 |
| Step 2 | 23.323808 |
| Step 3 | 23.323808 |
After 3 steps the estimate is 23.323808, matching √544 ≈ 23.323808.
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Frequently asked questions
Is 544 a perfect square?
No, 544 is not a perfect square, so its square root is irrational and approximately 23.323808.
What is the square root of 544 in simplest radical form?
√544 = 4√34 in simplest radical form.