Square Root Calculator › Square root of 598
Square Root of 598
√598 ≈ 24.454039
598 is not a perfect square, so √598 is an irrational number that is approximately 24.454039. In simplified radical form, √598 = √598.
√598 lies between √576 = 24 and √625 = 25.
| Number | 598 |
| Square root (decimal) | 24.454039 |
| Simplified radical | √598 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 598
598 = 2 × 13 × 23. This is what determines the simplified radical: for √598 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √598 is already in simplest radical form as √598.
Estimating √598 by hand
√598 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 598 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.458333 |
| Step 2 | 24.454039 |
| Step 3 | 24.454039 |
After 3 steps the estimate is 24.454039, matching √598 ≈ 24.454039.
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Frequently asked questions
Is 598 a perfect square?
No, 598 is not a perfect square, so its square root is irrational and approximately 24.454039.
What is the square root of 598 in simplest radical form?
√598 = √598 in simplest radical form.