Square Root Calculator › Square root of 281
Square Root of 281
√281 ≈ 16.763055
281 is not a perfect square, so √281 is an irrational number that is approximately 16.763055. In simplified radical form, √281 = √281.
√281 lies between √256 = 16 and √289 = 17.
| Number | 281 |
| Square root (decimal) | 16.763055 |
| Simplified radical | √281 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 281
281 = 281. This is what determines the simplified radical: for √281 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √281 is already in simplest radical form as √281.
Estimating √281 by hand
√281 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 281 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.78125 |
| Step 2 | 16.763064 |
| Step 3 | 16.763055 |
After 3 steps the estimate is 16.763055, matching √281 ≈ 16.763055.
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Frequently asked questions
Is 281 a perfect square?
No, 281 is not a perfect square, so its square root is irrational and approximately 16.763055.
What is the square root of 281 in simplest radical form?
√281 = √281 in simplest radical form.