Square Root Calculator › Square root of 162
Square Root of 162
√162 ≈ 12.727922
162 is not a perfect square, so √162 is an irrational number that is approximately 12.727922. In simplified radical form, √162 = 9√2.
√162 lies between √144 = 12 and √169 = 13.
| Number | 162 |
| Square root (decimal) | 12.727922 |
| Simplified radical | 9√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 162
162 = 2 × 3^4. This is what determines the simplified radical: for √162 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √162 = 9√2.
Estimating √162 by hand
√162 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 162 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.75 |
| Step 2 | 12.727941 |
| Step 3 | 12.727922 |
After 3 steps the estimate is 12.727922, matching √162 ≈ 12.727922.
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Frequently asked questions
Is 162 a perfect square?
No, 162 is not a perfect square, so its square root is irrational and approximately 12.727922.
What is the square root of 162 in simplest radical form?
√162 = 9√2 in simplest radical form.