Square root of 128
√128 ≈ 11.3137. The square root of 128 is about 11.3137, which simplifies to 8√2. 128 is not a perfect square, so √128 is irrational: its decimals never end or repeat.
| Value | 11.3137085 |
|---|---|
| Rounded | 11.3 (1 dp) · 11.31 (2 dp) · 11.314 (3 dp) |
| Simplest radical form | 8√2 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 128 squared | 16,384 |
Estimating √128 in your head
Start from the nearest perfect square, 11² = 121. 128 is 7 more than that. Divide the difference by twice the root, 22, and add it:
√128 ≈ 11 + 7 ÷ 22 ≈ 11.318
The true value is 11.3137, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 128 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √128
Find the largest perfect square that divides 128: it is 64, since 128 = 64 × 2. Take its root outside: √128 = √64 × √2 = 8√2.
Frequently asked questions
What is the square root of 128?
The square root of 128 is about 11.3137, which simplifies to 8√2. 128 is not a perfect square, so √128 is irrational: its decimals never end or repeat.
Is 128 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √128 in simplest radical form?
√128 = √(64 × 2) = 8√2.
Practise estimating square rootsNearby: √127 · √129 · all square roots to 150