Square Root Calculator › Square root of 272
Square Root of 272
√272 ≈ 16.492423
272 is not a perfect square, so √272 is an irrational number that is approximately 16.492423. In simplified radical form, √272 = 4√17.
√272 lies between √256 = 16 and √289 = 17.
| Number | 272 |
| Square root (decimal) | 16.492423 |
| Simplified radical | 4√17 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 272
272 = 2^4 × 17. This is what determines the simplified radical: for √272 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √272 = 4√17.
Estimating √272 by hand
√272 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 272 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.5 |
| Step 2 | 16.492424 |
| Step 3 | 16.492423 |
After 3 steps the estimate is 16.492423, matching √272 ≈ 16.492423.
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Frequently asked questions
Is 272 a perfect square?
No, 272 is not a perfect square, so its square root is irrational and approximately 16.492423.
What is the square root of 272 in simplest radical form?
√272 = 4√17 in simplest radical form.