Square Root Calculator › Square root of 284
Square Root of 284
√284 ≈ 16.8523
284 is not a perfect square, so √284 is an irrational number that is approximately 16.8523. In simplified radical form, √284 = 2√71.
√284 lies between √256 = 16 and √289 = 17.
| Number | 284 |
| Square root (decimal) | 16.8523 |
| Simplified radical | 2√71 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 284
284 = 2^2 × 71. This is what determines the simplified radical: for √284 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √284 = 2√71.
Estimating √284 by hand
√284 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 284 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.875 |
| Step 2 | 16.852315 |
| Step 3 | 16.8523 |
After 3 steps the estimate is 16.8523, matching √284 ≈ 16.8523.
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Frequently asked questions
Is 284 a perfect square?
No, 284 is not a perfect square, so its square root is irrational and approximately 16.8523.
What is the square root of 284 in simplest radical form?
√284 = 2√71 in simplest radical form.