Square Root Calculator › Square root of 282
Square Root of 282
√282 ≈ 16.792856
282 is not a perfect square, so √282 is an irrational number that is approximately 16.792856. In simplified radical form, √282 = √282.
√282 lies between √256 = 16 and √289 = 17.
| Number | 282 |
| Square root (decimal) | 16.792856 |
| Simplified radical | √282 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 282
282 = 2 × 3 × 47. This is what determines the simplified radical: for √282 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √282 is already in simplest radical form as √282.
Estimating √282 by hand
√282 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 282 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.8125 |
| Step 2 | 16.792867 |
| Step 3 | 16.792856 |
After 3 steps the estimate is 16.792856, matching √282 ≈ 16.792856.
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Frequently asked questions
Is 282 a perfect square?
No, 282 is not a perfect square, so its square root is irrational and approximately 16.792856.
What is the square root of 282 in simplest radical form?
√282 = √282 in simplest radical form.