Square Root Calculator › Square root of 285
Square Root of 285
√285 ≈ 16.881943
285 is not a perfect square, so √285 is an irrational number that is approximately 16.881943. In simplified radical form, √285 = √285.
√285 lies between √256 = 16 and √289 = 17.
| Number | 285 |
| Square root (decimal) | 16.881943 |
| Simplified radical | √285 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 285
285 = 3 × 5 × 19. This is what determines the simplified radical: for √285 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √285 is already in simplest radical form as √285.
Estimating √285 by hand
√285 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 285 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.90625 |
| Step 2 | 16.88196 |
| Step 3 | 16.881943 |
After 3 steps the estimate is 16.881943, matching √285 ≈ 16.881943.
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Frequently asked questions
Is 285 a perfect square?
No, 285 is not a perfect square, so its square root is irrational and approximately 16.881943.
What is the square root of 285 in simplest radical form?
√285 = √285 in simplest radical form.