√128 =
8√2
≈ 11.313708
Square root of 128 — 11.313708 (8√2)
Irrational
The square root of 128 is about 11.313708, or exactly 8√2. It lies between 11 and 12.
- As a decimal
- ≈ 11.313708
- Simplified surd
- √128 = 8√2
- Between
- 11 < √128 < 12
- Squared
- 128² = 16384
- Cube root
- ∛128 ≈ 5.039684
How the surd is simplified
Pull out the largest square factor. Since 50 = 25 × 2, the root of 25 comes out as 5 and the 2 stays behind: 5√2.
√128 = √(64 × 2) = 8√2
Nearby numbers
From 1 to 200
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How to read this
- The decimal is rounded; the surd form is the exact value.
- Pulling out a square factor simplifies the surd — √50 = 5√2.
- If the number is not a perfect square, the decimal never ends (irrational).
- Knowing which two integers it sits between is enough to estimate in your head.
Frequently asked questions
Q. What is the square root of 128?
About 11.313708, or exactly 8√2.
Q. Can the surd be simplified?
Yes: 128 = 64 × 2, so 8 comes out and it becomes 8√2.
Q. Between which integers does it fall?
Between 11 and 12.
Q. What is the cube root of 128?
About 5.039684.