Square Root Calculator › Square root of 237
Square Root of 237
√237 ≈ 15.394804
237 is not a perfect square, so √237 is an irrational number that is approximately 15.394804. In simplified radical form, √237 = √237.
√237 lies between √225 = 15 and √256 = 16.
| Number | 237 |
| Square root (decimal) | 15.394804 |
| Simplified radical | √237 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 237
237 = 3 × 79. This is what determines the simplified radical: for √237 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √237 is already in simplest radical form as √237.
Estimating √237 by hand
√237 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 237 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.4 |
| Step 2 | 15.394805 |
| Step 3 | 15.394804 |
After 3 steps the estimate is 15.394804, matching √237 ≈ 15.394804.
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Frequently asked questions
Is 237 a perfect square?
No, 237 is not a perfect square, so its square root is irrational and approximately 15.394804.
What is the square root of 237 in simplest radical form?
√237 = √237 in simplest radical form.