Square Root Calculator › Square root of 605
Square Root of 605
√605 ≈ 24.596748
605 is not a perfect square, so √605 is an irrational number that is approximately 24.596748. In simplified radical form, √605 = 11√5.
√605 lies between √576 = 24 and √625 = 25.
| Number | 605 |
| Square root (decimal) | 24.596748 |
| Simplified radical | 11√5 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 605
605 = 5 × 11^2. This is what determines the simplified radical: for √605 you pull out one copy of any prime that appears twice.
Here the paired factor 11 comes out from under the root, leaving √605 = 11√5.
Estimating √605 by hand
√605 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 605 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.604167 |
| Step 2 | 24.596749 |
| Step 3 | 24.596748 |
After 3 steps the estimate is 24.596748, matching √605 ≈ 24.596748.
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Frequently asked questions
Is 605 a perfect square?
No, 605 is not a perfect square, so its square root is irrational and approximately 24.596748.
What is the square root of 605 in simplest radical form?
√605 = 11√5 in simplest radical form.