Square Root Calculator › Square root of 238
Square Root of 238
√238 ≈ 15.427249
238 is not a perfect square, so √238 is an irrational number that is approximately 15.427249. In simplified radical form, √238 = √238.
√238 lies between √225 = 15 and √256 = 16.
| Number | 238 |
| Square root (decimal) | 15.427249 |
| Simplified radical | √238 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 238
238 = 2 × 7 × 17. This is what determines the simplified radical: for √238 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √238 is already in simplest radical form as √238.
Estimating √238 by hand
√238 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 238 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.433333 |
| Step 2 | 15.42725 |
| Step 3 | 15.427249 |
After 3 steps the estimate is 15.427249, matching √238 ≈ 15.427249.
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Frequently asked questions
Is 238 a perfect square?
No, 238 is not a perfect square, so its square root is irrational and approximately 15.427249.
What is the square root of 238 in simplest radical form?
√238 = √238 in simplest radical form.