Square Root Calculator › Square root of 283
Square Root of 283
√283 ≈ 16.822604
283 is not a perfect square, so √283 is an irrational number that is approximately 16.822604. In simplified radical form, √283 = √283.
√283 lies between √256 = 16 and √289 = 17.
| Number | 283 |
| Square root (decimal) | 16.822604 |
| Simplified radical | √283 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 283
283 = 283. This is what determines the simplified radical: for √283 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √283 is already in simplest radical form as √283.
Estimating √283 by hand
√283 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 283 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.84375 |
| Step 2 | 16.822617 |
| Step 3 | 16.822604 |
After 3 steps the estimate is 16.822604, matching √283 ≈ 16.822604.
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Frequently asked questions
Is 283 a perfect square?
No, 283 is not a perfect square, so its square root is irrational and approximately 16.822604.
What is the square root of 283 in simplest radical form?
√283 = √283 in simplest radical form.