Square Root Calculator › Square root of 11
Square Root of 11
√11 ≈ 3.316625
11 is not a perfect square, so √11 is an irrational number that is approximately 3.316625. In simplified radical form, √11 = √11.
√11 lies between √9 = 3 and √16 = 4.
| Number | 11 |
| Square root (decimal) | 3.316625 |
| Simplified radical | √11 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 11
11 = 11. This is what determines the simplified radical: for √11 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √11 is already in simplest radical form as √11.
Estimating √11 by hand
√11 falls between √9 = 3 and √16 = 4, so it starts at 3.something. The Babylonian method refines that guess by averaging it with 11 ÷ the guess:
| Step | Estimate |
| Start | 3 |
| Step 1 | 3.333333 |
| Step 2 | 3.316667 |
| Step 3 | 3.316625 |
After 3 steps the estimate is 3.316625, matching √11 ≈ 3.316625.
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Frequently asked questions
Is 11 a perfect square?
No, 11 is not a perfect square, so its square root is irrational and approximately 3.316625.
What is the square root of 11 in simplest radical form?
√11 = √11 in simplest radical form.