Square root of 136
√136 ≈ 11.6619. The square root of 136 is about 11.6619, which simplifies to 2√34. 136 is not a perfect square, so √136 is irrational: its decimals never end or repeat.
| Value | 11.66190379 |
|---|---|
| Rounded | 11.7 (1 dp) · 11.66 (2 dp) · 11.662 (3 dp) |
| Simplest radical form | 2√34 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 136 squared | 18,496 |
Estimating √136 in your head
Start from the nearest perfect square, 12² = 144. 136 is 8 less than that. Divide the difference by twice the root, 24, and subtract it:
√136 ≈ 12 − 8 ÷ 24 ≈ 11.667
The true value is 11.6619, so the one-step estimate is off by about 0.005. The estimate always comes out slightly high, and it is closest when 136 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √136
Find the largest perfect square that divides 136: it is 4, since 136 = 4 × 34. Take its root outside: √136 = √4 × √34 = 2√34.
Frequently asked questions
What is the square root of 136?
The square root of 136 is about 11.6619, which simplifies to 2√34. 136 is not a perfect square, so √136 is irrational: its decimals never end or repeat.
Is 136 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √136 in simplest radical form?
√136 = √(4 × 34) = 2√34.
Practise estimating square rootsNearby: √135 · √137 · all square roots to 150