Square Root Calculator › Square root of 190
Square Root of 190
√190 ≈ 13.784049
190 is not a perfect square, so √190 is an irrational number that is approximately 13.784049. In simplified radical form, √190 = √190.
√190 lies between √169 = 13 and √196 = 14.
| Number | 190 |
| Square root (decimal) | 13.784049 |
| Simplified radical | √190 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 190
190 = 2 × 5 × 19. This is what determines the simplified radical: for √190 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √190 is already in simplest radical form as √190.
Estimating √190 by hand
√190 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 190 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.807692 |
| Step 2 | 13.784069 |
| Step 3 | 13.784049 |
After 3 steps the estimate is 13.784049, matching √190 ≈ 13.784049.
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Frequently asked questions
Is 190 a perfect square?
No, 190 is not a perfect square, so its square root is irrational and approximately 13.784049.
What is the square root of 190 in simplest radical form?
√190 = √190 in simplest radical form.