Square Root Calculator › Square root of 194
Square Root of 194
√194 ≈ 13.928388
194 is not a perfect square, so √194 is an irrational number that is approximately 13.928388. In simplified radical form, √194 = √194.
√194 lies between √169 = 13 and √196 = 14.
| Number | 194 |
| Square root (decimal) | 13.928388 |
| Simplified radical | √194 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 194
194 = 2 × 97. This is what determines the simplified radical: for √194 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √194 is already in simplest radical form as √194.
Estimating √194 by hand
√194 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 194 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.961538 |
| Step 2 | 13.928428 |
| Step 3 | 13.928388 |
After 3 steps the estimate is 13.928388, matching √194 ≈ 13.928388.
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Frequently asked questions
Is 194 a perfect square?
No, 194 is not a perfect square, so its square root is irrational and approximately 13.928388.
What is the square root of 194 in simplest radical form?
√194 = √194 in simplest radical form.