Square Root Calculator › Square root of 254
Square Root of 254
√254 ≈ 15.937377
254 is not a perfect square, so √254 is an irrational number that is approximately 15.937377. In simplified radical form, √254 = √254.
√254 lies between √225 = 15 and √256 = 16.
| Number | 254 |
| Square root (decimal) | 15.937377 |
| Simplified radical | √254 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 254
254 = 2 × 127. This is what determines the simplified radical: for √254 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √254 is already in simplest radical form as √254.
Estimating √254 by hand
√254 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 254 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.966667 |
| Step 2 | 15.937404 |
| Step 3 | 15.937377 |
After 3 steps the estimate is 15.937377, matching √254 ≈ 15.937377.
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Frequently asked questions
Is 254 a perfect square?
No, 254 is not a perfect square, so its square root is irrational and approximately 15.937377.
What is the square root of 254 in simplest radical form?
√254 = √254 in simplest radical form.