Square Root Calculator › Square root of 226
Square Root of 226
√226 ≈ 15.033296
226 is not a perfect square, so √226 is an irrational number that is approximately 15.033296. In simplified radical form, √226 = √226.
√226 lies between √225 = 15 and √256 = 16.
| Number | 226 |
| Square root (decimal) | 15.033296 |
| Simplified radical | √226 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 226
226 = 2 × 113. This is what determines the simplified radical: for √226 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √226 is already in simplest radical form as √226.
Estimating √226 by hand
√226 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 226 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.033333 |
| Step 2 | 15.033296 |
| Step 3 | 15.033296 |
After 3 steps the estimate is 15.033296, matching √226 ≈ 15.033296.
Nearby square roots
Frequently asked questions
Is 226 a perfect square?
No, 226 is not a perfect square, so its square root is irrational and approximately 15.033296.
What is the square root of 226 in simplest radical form?
√226 = √226 in simplest radical form.