Square Root Calculator › Square root of 275
Square Root of 275
√275 ≈ 16.583124
275 is not a perfect square, so √275 is an irrational number that is approximately 16.583124. In simplified radical form, √275 = 5√11.
√275 lies between √256 = 16 and √289 = 17.
| Number | 275 |
| Square root (decimal) | 16.583124 |
| Simplified radical | 5√11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 275
275 = 5^2 × 11. This is what determines the simplified radical: for √275 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √275 = 5√11.
Estimating √275 by hand
√275 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 275 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.59375 |
| Step 2 | 16.583127 |
| Step 3 | 16.583124 |
After 3 steps the estimate is 16.583124, matching √275 ≈ 16.583124.
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Frequently asked questions
Is 275 a perfect square?
No, 275 is not a perfect square, so its square root is irrational and approximately 16.583124.
What is the square root of 275 in simplest radical form?
√275 = 5√11 in simplest radical form.