Square Root Calculator › Square root of 609
Square Root of 609
√609 ≈ 24.677925
609 is not a perfect square, so √609 is an irrational number that is approximately 24.677925. In simplified radical form, √609 = √609.
√609 lies between √576 = 24 and √625 = 25.
| Number | 609 |
| Square root (decimal) | 24.677925 |
| Simplified radical | √609 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 609
609 = 3 × 7 × 29. This is what determines the simplified radical: for √609 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √609 is already in simplest radical form as √609.
Estimating √609 by hand
√609 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 609 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.6875 |
| Step 2 | 24.677927 |
| Step 3 | 24.677925 |
After 3 steps the estimate is 24.677925, matching √609 ≈ 24.677925.
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Frequently asked questions
Is 609 a perfect square?
No, 609 is not a perfect square, so its square root is irrational and approximately 24.677925.
What is the square root of 609 in simplest radical form?
√609 = √609 in simplest radical form.