Square Root Calculator › Square root of 610
Square Root of 610
√610 ≈ 24.698178
610 is not a perfect square, so √610 is an irrational number that is approximately 24.698178. In simplified radical form, √610 = √610.
√610 lies between √576 = 24 and √625 = 25.
| Number | 610 |
| Square root (decimal) | 24.698178 |
| Simplified radical | √610 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 610
610 = 2 × 5 × 61. This is what determines the simplified radical: for √610 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √610 is already in simplest radical form as √610.
Estimating √610 by hand
√610 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 610 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.708333 |
| Step 2 | 24.69818 |
| Step 3 | 24.698178 |
After 3 steps the estimate is 24.698178, matching √610 ≈ 24.698178.
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Frequently asked questions
Is 610 a perfect square?
No, 610 is not a perfect square, so its square root is irrational and approximately 24.698178.
What is the square root of 610 in simplest radical form?
√610 = √610 in simplest radical form.