Square Root Calculator › Square root of 187
Square Root of 187
√187 ≈ 13.674794
187 is not a perfect square, so √187 is an irrational number that is approximately 13.674794. In simplified radical form, √187 = √187.
√187 lies between √169 = 13 and √196 = 14.
| Number | 187 |
| Square root (decimal) | 13.674794 |
| Simplified radical | √187 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 187
187 = 11 × 17. This is what determines the simplified radical: for √187 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √187 is already in simplest radical form as √187.
Estimating √187 by hand
√187 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 187 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.692308 |
| Step 2 | 13.674806 |
| Step 3 | 13.674794 |
After 3 steps the estimate is 13.674794, matching √187 ≈ 13.674794.
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Frequently asked questions
Is 187 a perfect square?
No, 187 is not a perfect square, so its square root is irrational and approximately 13.674794.
What is the square root of 187 in simplest radical form?
√187 = √187 in simplest radical form.