Square Root Calculator › Square root of 606
Square Root of 606
√606 ≈ 24.617067
606 is not a perfect square, so √606 is an irrational number that is approximately 24.617067. In simplified radical form, √606 = √606.
√606 lies between √576 = 24 and √625 = 25.
| Number | 606 |
| Square root (decimal) | 24.617067 |
| Simplified radical | √606 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 606
606 = 2 × 3 × 101. This is what determines the simplified radical: for √606 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √606 is already in simplest radical form as √606.
Estimating √606 by hand
√606 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 606 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.625 |
| Step 2 | 24.617069 |
| Step 3 | 24.617067 |
After 3 steps the estimate is 24.617067, matching √606 ≈ 24.617067.
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Frequently asked questions
Is 606 a perfect square?
No, 606 is not a perfect square, so its square root is irrational and approximately 24.617067.
What is the square root of 606 in simplest radical form?
√606 = √606 in simplest radical form.