Square Root Calculator › Square root of 612
Square Root of 612
√612 ≈ 24.738634
612 is not a perfect square, so √612 is an irrational number that is approximately 24.738634. In simplified radical form, √612 = 6√17.
√612 lies between √576 = 24 and √625 = 25.
| Number | 612 |
| Square root (decimal) | 24.738634 |
| Simplified radical | 6√17 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 612
612 = 2^2 × 3^2 × 17. This is what determines the simplified radical: for √612 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √612 = 6√17.
Estimating √612 by hand
√612 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 612 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.75 |
| Step 2 | 24.738636 |
| Step 3 | 24.738634 |
After 3 steps the estimate is 24.738634, matching √612 ≈ 24.738634.
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Frequently asked questions
Is 612 a perfect square?
No, 612 is not a perfect square, so its square root is irrational and approximately 24.738634.
What is the square root of 612 in simplest radical form?
√612 = 6√17 in simplest radical form.