Square Root Calculator › Square root of 198
Square Root of 198
√198 ≈ 14.071247
198 is not a perfect square, so √198 is an irrational number that is approximately 14.071247. In simplified radical form, √198 = 3√22.
√198 lies between √196 = 14 and √225 = 15.
| Number | 198 |
| Square root (decimal) | 14.071247 |
| Simplified radical | 3√22 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 198
198 = 2 × 3^2 × 11. This is what determines the simplified radical: for √198 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √198 = 3√22.
Estimating √198 by hand
√198 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 198 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.071429 |
| Step 2 | 14.071247 |
| Step 3 | 14.071247 |
After 3 steps the estimate is 14.071247, matching √198 ≈ 14.071247.
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Frequently asked questions
Is 198 a perfect square?
No, 198 is not a perfect square, so its square root is irrational and approximately 14.071247.
What is the square root of 198 in simplest radical form?
√198 = 3√22 in simplest radical form.