Square Root Calculator › Square root of 193
Square Root of 193
√193 ≈ 13.892444
193 is not a perfect square, so √193 is an irrational number that is approximately 13.892444. In simplified radical form, √193 = √193.
√193 lies between √169 = 13 and √196 = 14.
| Number | 193 |
| Square root (decimal) | 13.892444 |
| Simplified radical | √193 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 193
193 = 193. This is what determines the simplified radical: for √193 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √193 is already in simplest radical form as √193.
Estimating √193 by hand
√193 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 193 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.923077 |
| Step 2 | 13.892478 |
| Step 3 | 13.892444 |
After 3 steps the estimate is 13.892444, matching √193 ≈ 13.892444.
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Frequently asked questions
Is 193 a perfect square?
No, 193 is not a perfect square, so its square root is irrational and approximately 13.892444.
What is the square root of 193 in simplest radical form?
√193 = √193 in simplest radical form.