Square Root Calculator › Square root of 263
Square Root of 263
√263 ≈ 16.217275
263 is not a perfect square, so √263 is an irrational number that is approximately 16.217275. In simplified radical form, √263 = √263.
√263 lies between √256 = 16 and √289 = 17.
| Number | 263 |
| Square root (decimal) | 16.217275 |
| Simplified radical | √263 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 263
263 = 263. This is what determines the simplified radical: for √263 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √263 is already in simplest radical form as √263.
Estimating √263 by hand
√263 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 263 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.21875 |
| Step 2 | 16.217275 |
| Step 3 | 16.217275 |
After 3 steps the estimate is 16.217275, matching √263 ≈ 16.217275.
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Frequently asked questions
Is 263 a perfect square?
No, 263 is not a perfect square, so its square root is irrational and approximately 16.217275.
What is the square root of 263 in simplest radical form?
√263 = √263 in simplest radical form.