Square Root Calculator › Square root of 287
Square Root of 287
√287 ≈ 16.941074
287 is not a perfect square, so √287 is an irrational number that is approximately 16.941074. In simplified radical form, √287 = √287.
√287 lies between √256 = 16 and √289 = 17.
| Number | 287 |
| Square root (decimal) | 16.941074 |
| Simplified radical | √287 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 287
287 = 7 × 41. This is what determines the simplified radical: for √287 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √287 is already in simplest radical form as √287.
Estimating √287 by hand
√287 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 287 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.96875 |
| Step 2 | 16.941097 |
| Step 3 | 16.941074 |
After 3 steps the estimate is 16.941074, matching √287 ≈ 16.941074.
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Frequently asked questions
Is 287 a perfect square?
No, 287 is not a perfect square, so its square root is irrational and approximately 16.941074.
What is the square root of 287 in simplest radical form?
√287 = √287 in simplest radical form.