Square Root Calculator › Square root of 608
Square Root of 608
√608 ≈ 24.657656
608 is not a perfect square, so √608 is an irrational number that is approximately 24.657656. In simplified radical form, √608 = 4√38.
√608 lies between √576 = 24 and √625 = 25.
| Number | 608 |
| Square root (decimal) | 24.657656 |
| Simplified radical | 4√38 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 608
608 = 2^5 × 19. This is what determines the simplified radical: for √608 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √608 = 4√38.
Estimating √608 by hand
√608 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 608 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.666667 |
| Step 2 | 24.657658 |
| Step 3 | 24.657656 |
After 3 steps the estimate is 24.657656, matching √608 ≈ 24.657656.
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Frequently asked questions
Is 608 a perfect square?
No, 608 is not a perfect square, so its square root is irrational and approximately 24.657656.
What is the square root of 608 in simplest radical form?
√608 = 4√38 in simplest radical form.