Square Root Calculator › Square root of 221
Square Root of 221
√221 ≈ 14.866069
221 is not a perfect square, so √221 is an irrational number that is approximately 14.866069. In simplified radical form, √221 = √221.
√221 lies between √196 = 14 and √225 = 15.
| Number | 221 |
| Square root (decimal) | 14.866069 |
| Simplified radical | √221 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 221
221 = 13 × 17. This is what determines the simplified radical: for √221 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √221 is already in simplest radical form as √221.
Estimating √221 by hand
√221 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 221 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.892857 |
| Step 2 | 14.866093 |
| Step 3 | 14.866069 |
After 3 steps the estimate is 14.866069, matching √221 ≈ 14.866069.
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Frequently asked questions
Is 221 a perfect square?
No, 221 is not a perfect square, so its square root is irrational and approximately 14.866069.
What is the square root of 221 in simplest radical form?
√221 = √221 in simplest radical form.