Square Root Calculator › Square root of 613
Square Root of 613
√613 ≈ 24.758837
613 is not a perfect square, so √613 is an irrational number that is approximately 24.758837. In simplified radical form, √613 = √613.
√613 lies between √576 = 24 and √625 = 25.
| Number | 613 |
| Square root (decimal) | 24.758837 |
| Simplified radical | √613 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 613
613 = 613. This is what determines the simplified radical: for √613 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √613 is already in simplest radical form as √613.
Estimating √613 by hand
√613 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 613 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.770833 |
| Step 2 | 24.75884 |
| Step 3 | 24.758837 |
After 3 steps the estimate is 24.758837, matching √613 ≈ 24.758837.
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Frequently asked questions
Is 613 a perfect square?
No, 613 is not a perfect square, so its square root is irrational and approximately 24.758837.
What is the square root of 613 in simplest radical form?
√613 = √613 in simplest radical form.