Square root of 139
√139 ≈ 11.7898. The square root of 139 is about 11.7898. 139 is not a perfect square, so √139 is irrational: its decimals never end or repeat.
| Value | 11.78982612 |
|---|---|
| Rounded | 11.8 (1 dp) · 11.79 (2 dp) · 11.790 (3 dp) |
| Simplest radical form | √139 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 139 squared | 19,321 |
Estimating √139 in your head
Start from the nearest perfect square, 12² = 144. 139 is 5 less than that. Divide the difference by twice the root, 24, and subtract it:
√139 ≈ 12 − 5 ÷ 24 ≈ 11.792
The true value is 11.7898, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 139 is near a perfect square. The method is explained in estimating square roots in your head.
Can √139 be simplified?
No. 139 has no perfect-square factor besides 1, so √139 is already in simplest radical form.
Frequently asked questions
What is the square root of 139?
The square root of 139 is about 11.7898. 139 is not a perfect square, so √139 is irrational: its decimals never end or repeat.
Is 139 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √139 in simplest radical form?
√139 is already in simplest form: 139 has no square factor other than 1.
Practise estimating square rootsNearby: √138 · √140 · all square roots to 150