Square root of 140
√140 ≈ 11.8322. The square root of 140 is about 11.8322, which simplifies to 2√35. 140 is not a perfect square, so √140 is irrational: its decimals never end or repeat.
| Value | 11.83215957 |
|---|---|
| Rounded | 11.8 (1 dp) · 11.83 (2 dp) · 11.832 (3 dp) |
| Simplest radical form | 2√35 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 140 squared | 19,600 |
Estimating √140 in your head
Start from the nearest perfect square, 12² = 144. 140 is 4 less than that. Divide the difference by twice the root, 24, and subtract it:
√140 ≈ 12 − 4 ÷ 24 ≈ 11.833
The true value is 11.8322, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 140 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √140
Find the largest perfect square that divides 140: it is 4, since 140 = 4 × 35. Take its root outside: √140 = √4 × √35 = 2√35.
Frequently asked questions
What is the square root of 140?
The square root of 140 is about 11.8322, which simplifies to 2√35. 140 is not a perfect square, so √140 is irrational: its decimals never end or repeat.
Is 140 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √140 in simplest radical form?
√140 = √(4 × 35) = 2√35.
Practise estimating square rootsNearby: √139 · √141 · all square roots to 150