Square Root Calculator › Square root of 211
Square Root of 211
√211 ≈ 14.525839
211 is not a perfect square, so √211 is an irrational number that is approximately 14.525839. In simplified radical form, √211 = √211.
√211 lies between √196 = 14 and √225 = 15.
| Number | 211 |
| Square root (decimal) | 14.525839 |
| Simplified radical | √211 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 211
211 = 211. This is what determines the simplified radical: for √211 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √211 is already in simplest radical form as √211.
Estimating √211 by hand
√211 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 211 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.535714 |
| Step 2 | 14.525842 |
| Step 3 | 14.525839 |
After 3 steps the estimate is 14.525839, matching √211 ≈ 14.525839.
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Frequently asked questions
Is 211 a perfect square?
No, 211 is not a perfect square, so its square root is irrational and approximately 14.525839.
What is the square root of 211 in simplest radical form?
√211 = √211 in simplest radical form.