Square Root Calculator › Square root of 255
Square Root of 255
√255 ≈ 15.968719
255 is not a perfect square, so √255 is an irrational number that is approximately 15.968719. In simplified radical form, √255 = √255.
√255 lies between √225 = 15 and √256 = 16.
| Number | 255 |
| Square root (decimal) | 15.968719 |
| Simplified radical | √255 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 255
255 = 3 × 5 × 17. This is what determines the simplified radical: for √255 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √255 is already in simplest radical form as √255.
Estimating √255 by hand
√255 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 255 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 16 |
| Step 2 | 15.96875 |
| Step 3 | 15.968719 |
After 3 steps the estimate is 15.968719, matching √255 ≈ 15.968719.
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Frequently asked questions
Is 255 a perfect square?
No, 255 is not a perfect square, so its square root is irrational and approximately 15.968719.
What is the square root of 255 in simplest radical form?
√255 = √255 in simplest radical form.