Square Root Calculator › Square root of 171
Square Root of 171
√171 ≈ 13.076697
171 is not a perfect square, so √171 is an irrational number that is approximately 13.076697. In simplified radical form, √171 = 3√19.
√171 lies between √169 = 13 and √196 = 14.
| Number | 171 |
| Square root (decimal) | 13.076697 |
| Simplified radical | 3√19 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 171
171 = 3^2 × 19. This is what determines the simplified radical: for √171 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √171 = 3√19.
Estimating √171 by hand
√171 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 171 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.076923 |
| Step 2 | 13.076697 |
| Step 3 | 13.076697 |
After 3 steps the estimate is 13.076697, matching √171 ≈ 13.076697.
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Frequently asked questions
Is 171 a perfect square?
No, 171 is not a perfect square, so its square root is irrational and approximately 13.076697.
What is the square root of 171 in simplest radical form?
√171 = 3√19 in simplest radical form.