Square Root Calculator › Square root of 128
Square Root of 128
√128 ≈ 11.313708
128 is not a perfect square, so √128 is an irrational number that is approximately 11.313708. In simplified radical form, √128 = 8√2.
√128 lies between √121 = 11 and √144 = 12.
| Number | 128 |
| Square root (decimal) | 11.313708 |
| Simplified radical | 8√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 128
128 = 2^7. This is what determines the simplified radical: for √128 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √128 = 8√2.
Estimating √128 by hand
√128 falls between √121 = 11 and √144 = 12, so it starts at 11.something. The Babylonian method refines that guess by averaging it with 128 ÷ the guess:
| Step | Estimate |
| Start | 11 |
| Step 1 | 11.318182 |
| Step 2 | 11.313709 |
| Step 3 | 11.313708 |
After 3 steps the estimate is 11.313708, matching √128 ≈ 11.313708.
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Frequently asked questions
Is 128 a perfect square?
No, 128 is not a perfect square, so its square root is irrational and approximately 11.313708.
What is the square root of 128 in simplest radical form?
√128 = 8√2 in simplest radical form.