Square Root Calculator › Square root of 186
Square Root of 186
√186 ≈ 13.638182
186 is not a perfect square, so √186 is an irrational number that is approximately 13.638182. In simplified radical form, √186 = √186.
√186 lies between √169 = 13 and √196 = 14.
| Number | 186 |
| Square root (decimal) | 13.638182 |
| Simplified radical | √186 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 186
186 = 2 × 3 × 31. This is what determines the simplified radical: for √186 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √186 is already in simplest radical form as √186.
Estimating √186 by hand
√186 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 186 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.653846 |
| Step 2 | 13.638191 |
| Step 3 | 13.638182 |
After 3 steps the estimate is 13.638182, matching √186 ≈ 13.638182.
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Frequently asked questions
Is 186 a perfect square?
No, 186 is not a perfect square, so its square root is irrational and approximately 13.638182.
What is the square root of 186 in simplest radical form?
√186 = √186 in simplest radical form.