Square Root Calculator › Square root of 136
Square Root of 136
√136 ≈ 11.661904
136 is not a perfect square, so √136 is an irrational number that is approximately 11.661904. In simplified radical form, √136 = 2√34.
√136 lies between √121 = 11 and √144 = 12.
| Number | 136 |
| Square root (decimal) | 11.661904 |
| Simplified radical | 2√34 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 136
136 = 2^3 × 17. This is what determines the simplified radical: for √136 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √136 = 2√34.
Estimating √136 by hand
√136 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 136 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.681818 |
| Step 2 | 11.661921 |
| Step 3 | 11.661904 |
After 3 steps the estimate is 11.661904, matching √136 ≈ 11.661904.
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Frequently asked questions
Is 136 a perfect square?
No, 136 is not a perfect square, so its square root is irrational and approximately 11.661904.
What is the square root of 136 in simplest radical form?
√136 = 2√34 in simplest radical form.