Square Root Calculator › Square root of 288
Square Root of 288
√288 ≈ 16.970563
288 is not a perfect square, so √288 is an irrational number that is approximately 16.970563. In simplified radical form, √288 = 12√2.
√288 lies between √256 = 16 and √289 = 17.
| Number | 288 |
| Square root (decimal) | 16.970563 |
| Simplified radical | 12√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 288
288 = 2^5 × 3^2. This is what determines the simplified radical: for √288 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √288 = 12√2.
Estimating √288 by hand
√288 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 288 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 17 |
| Step 2 | 16.970588 |
| Step 3 | 16.970563 |
After 3 steps the estimate is 16.970563, matching √288 ≈ 16.970563.
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Frequently asked questions
Is 288 a perfect square?
No, 288 is not a perfect square, so its square root is irrational and approximately 16.970563.
What is the square root of 288 in simplest radical form?
√288 = 12√2 in simplest radical form.