Square Root Calculator › Square root of 197
Square Root of 197
√197 ≈ 14.035669
197 is not a perfect square, so √197 is an irrational number that is approximately 14.035669. In simplified radical form, √197 = √197.
√197 lies between √196 = 14 and √225 = 15.
| Number | 197 |
| Square root (decimal) | 14.035669 |
| Simplified radical | √197 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 197
197 = 197. This is what determines the simplified radical: for √197 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √197 is already in simplest radical form as √197.
Estimating √197 by hand
√197 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 197 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.035714 |
| Step 2 | 14.035669 |
| Step 3 | 14.035669 |
After 3 steps the estimate is 14.035669, matching √197 ≈ 14.035669.
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Frequently asked questions
Is 197 a perfect square?
No, 197 is not a perfect square, so its square root is irrational and approximately 14.035669.
What is the square root of 197 in simplest radical form?
√197 = √197 in simplest radical form.