Square Root Calculator › Square root of 604
Square Root of 604
√604 ≈ 24.576411
604 is not a perfect square, so √604 is an irrational number that is approximately 24.576411. In simplified radical form, √604 = 2√151.
√604 lies between √576 = 24 and √625 = 25.
| Number | 604 |
| Square root (decimal) | 24.576411 |
| Simplified radical | 2√151 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 604
604 = 2^2 × 151. This is what determines the simplified radical: for √604 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √604 = 2√151.
Estimating √604 by hand
√604 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 604 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.583333 |
| Step 2 | 24.576412 |
| Step 3 | 24.576411 |
After 3 steps the estimate is 24.576411, matching √604 ≈ 24.576411.
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Frequently asked questions
Is 604 a perfect square?
No, 604 is not a perfect square, so its square root is irrational and approximately 24.576411.
What is the square root of 604 in simplest radical form?
√604 = 2√151 in simplest radical form.