Square Root Calculator › Square root of 262
Square Root of 262
√262 ≈ 16.186414
262 is not a perfect square, so √262 is an irrational number that is approximately 16.186414. In simplified radical form, √262 = √262.
√262 lies between √256 = 16 and √289 = 17.
| Number | 262 |
| Square root (decimal) | 16.186414 |
| Simplified radical | √262 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 262
262 = 2 × 131. This is what determines the simplified radical: for √262 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √262 is already in simplest radical form as √262.
Estimating √262 by hand
√262 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 262 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.1875 |
| Step 2 | 16.186414 |
| Step 3 | 16.186414 |
After 3 steps the estimate is 16.186414, matching √262 ≈ 16.186414.
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Frequently asked questions
Is 262 a perfect square?
No, 262 is not a perfect square, so its square root is irrational and approximately 16.186414.
What is the square root of 262 in simplest radical form?
√262 = √262 in simplest radical form.