Square Root Calculator › Square root of 161
Square Root of 161
√161 ≈ 12.688578
161 is not a perfect square, so √161 is an irrational number that is approximately 12.688578. In simplified radical form, √161 = √161.
√161 lies between √144 = 12 and √169 = 13.
| Number | 161 |
| Square root (decimal) | 12.688578 |
| Simplified radical | √161 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 161
161 = 7 × 23. This is what determines the simplified radical: for √161 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √161 is already in simplest radical form as √161.
Estimating √161 by hand
√161 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 161 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.708333 |
| Step 2 | 12.688593 |
| Step 3 | 12.688578 |
After 3 steps the estimate is 12.688578, matching √161 ≈ 12.688578.
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Frequently asked questions
Is 161 a perfect square?
No, 161 is not a perfect square, so its square root is irrational and approximately 12.688578.
What is the square root of 161 in simplest radical form?
√161 = √161 in simplest radical form.