Square Root Calculator › Square root of 614
Square Root of 614
√614 ≈ 24.779023
614 is not a perfect square, so √614 is an irrational number that is approximately 24.779023. In simplified radical form, √614 = √614.
√614 lies between √576 = 24 and √625 = 25.
| Number | 614 |
| Square root (decimal) | 24.779023 |
| Simplified radical | √614 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 614
614 = 2 × 307. This is what determines the simplified radical: for √614 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √614 is already in simplest radical form as √614.
Estimating √614 by hand
√614 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 614 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.791667 |
| Step 2 | 24.779027 |
| Step 3 | 24.779023 |
After 3 steps the estimate is 24.779023, matching √614 ≈ 24.779023.
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Frequently asked questions
Is 614 a perfect square?
No, 614 is not a perfect square, so its square root is irrational and approximately 24.779023.
What is the square root of 614 in simplest radical form?
√614 = √614 in simplest radical form.