Square Root Calculator › Square root of 164
Square Root of 164
√164 ≈ 12.806248
164 is not a perfect square, so √164 is an irrational number that is approximately 12.806248. In simplified radical form, √164 = 2√41.
√164 lies between √144 = 12 and √169 = 13.
| Number | 164 |
| Square root (decimal) | 12.806248 |
| Simplified radical | 2√41 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 164
164 = 2^2 × 41. This is what determines the simplified radical: for √164 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √164 = 2√41.
Estimating √164 by hand
√164 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 164 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.833333 |
| Step 2 | 12.806277 |
| Step 3 | 12.806248 |
After 3 steps the estimate is 12.806248, matching √164 ≈ 12.806248.
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Frequently asked questions
Is 164 a perfect square?
No, 164 is not a perfect square, so its square root is irrational and approximately 12.806248.
What is the square root of 164 in simplest radical form?
√164 = 2√41 in simplest radical form.