Square Root Calculator › Square root of 201
Square Root of 201
√201 ≈ 14.177447
201 is not a perfect square, so √201 is an irrational number that is approximately 14.177447. In simplified radical form, √201 = √201.
√201 lies between √196 = 14 and √225 = 15.
| Number | 201 |
| Square root (decimal) | 14.177447 |
| Simplified radical | √201 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 201
201 = 3 × 67. This is what determines the simplified radical: for √201 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √201 is already in simplest radical form as √201.
Estimating √201 by hand
√201 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 201 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.178571 |
| Step 2 | 14.177447 |
| Step 3 | 14.177447 |
After 3 steps the estimate is 14.177447, matching √201 ≈ 14.177447.
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Frequently asked questions
Is 201 a perfect square?
No, 201 is not a perfect square, so its square root is irrational and approximately 14.177447.
What is the square root of 201 in simplest radical form?
√201 = √201 in simplest radical form.