Square Root Calculator › Square root of 578
Square Root of 578
√578 ≈ 24.041631
578 is not a perfect square, so √578 is an irrational number that is approximately 24.041631. In simplified radical form, √578 = 17√2.
√578 lies between √576 = 24 and √625 = 25.
| Number | 578 |
| Square root (decimal) | 24.041631 |
| Simplified radical | 17√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 578
578 = 2 × 17^2. This is what determines the simplified radical: for √578 you pull out one copy of any prime that appears twice.
Here the paired factor 17 comes out from under the root, leaving √578 = 17√2.
Estimating √578 by hand
√578 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 578 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.041667 |
| Step 2 | 24.041631 |
| Step 3 | 24.041631 |
After 3 steps the estimate is 24.041631, matching √578 ≈ 24.041631.
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Frequently asked questions
Is 578 a perfect square?
No, 578 is not a perfect square, so its square root is irrational and approximately 24.041631.
What is the square root of 578 in simplest radical form?
√578 = 17√2 in simplest radical form.