Square Root Calculator › Square root of 239
Square Root of 239
√239 ≈ 15.459625
239 is not a perfect square, so √239 is an irrational number that is approximately 15.459625. In simplified radical form, √239 = √239.
√239 lies between √225 = 15 and √256 = 16.
| Number | 239 |
| Square root (decimal) | 15.459625 |
| Simplified radical | √239 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 239
239 = 239. This is what determines the simplified radical: for √239 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √239 is already in simplest radical form as √239.
Estimating √239 by hand
√239 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 239 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.466667 |
| Step 2 | 15.459626 |
| Step 3 | 15.459625 |
After 3 steps the estimate is 15.459625, matching √239 ≈ 15.459625.
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Frequently asked questions
Is 239 a perfect square?
No, 239 is not a perfect square, so its square root is irrational and approximately 15.459625.
What is the square root of 239 in simplest radical form?
√239 = √239 in simplest radical form.