Square Root Calculator › Square root of 167
Square Root of 167
√167 ≈ 12.922848
167 is not a perfect square, so √167 is an irrational number that is approximately 12.922848. In simplified radical form, √167 = √167.
√167 lies between √144 = 12 and √169 = 13.
| Number | 167 |
| Square root (decimal) | 12.922848 |
| Simplified radical | √167 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 167
167 = 167. This is what determines the simplified radical: for √167 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √167 is already in simplest radical form as √167.
Estimating √167 by hand
√167 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 167 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.958333 |
| Step 2 | 12.922897 |
| Step 3 | 12.922848 |
After 3 steps the estimate is 12.922848, matching √167 ≈ 12.922848.
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Frequently asked questions
Is 167 a perfect square?
No, 167 is not a perfect square, so its square root is irrational and approximately 12.922848.
What is the square root of 167 in simplest radical form?
√167 = √167 in simplest radical form.