Square Root Calculator › Square root of 185
Square Root of 185
√185 ≈ 13.601471
185 is not a perfect square, so √185 is an irrational number that is approximately 13.601471. In simplified radical form, √185 = √185.
√185 lies between √169 = 13 and √196 = 14.
| Number | 185 |
| Square root (decimal) | 13.601471 |
| Simplified radical | √185 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 185
185 = 5 × 37. This is what determines the simplified radical: for √185 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √185 is already in simplest radical form as √185.
Estimating √185 by hand
√185 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 185 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.615385 |
| Step 2 | 13.601478 |
| Step 3 | 13.601471 |
After 3 steps the estimate is 13.601471, matching √185 ≈ 13.601471.
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Frequently asked questions
Is 185 a perfect square?
No, 185 is not a perfect square, so its square root is irrational and approximately 13.601471.
What is the square root of 185 in simplest radical form?
√185 = √185 in simplest radical form.