Square Root Calculator › Square root of 166
Square Root of 166
√166 ≈ 12.884099
166 is not a perfect square, so √166 is an irrational number that is approximately 12.884099. In simplified radical form, √166 = √166.
√166 lies between √144 = 12 and √169 = 13.
| Number | 166 |
| Square root (decimal) | 12.884099 |
| Simplified radical | √166 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 166
166 = 2 × 83. This is what determines the simplified radical: for √166 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √166 is already in simplest radical form as √166.
Estimating √166 by hand
√166 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 166 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.916667 |
| Step 2 | 12.88414 |
| Step 3 | 12.884099 |
After 3 steps the estimate is 12.884099, matching √166 ≈ 12.884099.
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Frequently asked questions
Is 166 a perfect square?
No, 166 is not a perfect square, so its square root is irrational and approximately 12.884099.
What is the square root of 166 in simplest radical form?
√166 = √166 in simplest radical form.