Square Root Calculator › Square root of 230
Square Root of 230
√230 ≈ 15.165751
230 is not a perfect square, so √230 is an irrational number that is approximately 15.165751. In simplified radical form, √230 = √230.
√230 lies between √225 = 15 and √256 = 16.
| Number | 230 |
| Square root (decimal) | 15.165751 |
| Simplified radical | √230 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 230
230 = 2 × 5 × 23. This is what determines the simplified radical: for √230 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √230 is already in simplest radical form as √230.
Estimating √230 by hand
√230 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 230 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.166667 |
| Step 2 | 15.165751 |
| Step 3 | 15.165751 |
After 3 steps the estimate is 15.165751, matching √230 ≈ 15.165751.
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Frequently asked questions
Is 230 a perfect square?
No, 230 is not a perfect square, so its square root is irrational and approximately 15.165751.
What is the square root of 230 in simplest radical form?
√230 = √230 in simplest radical form.