Square root of 138
√138 ≈ 11.7473. The square root of 138 is about 11.7473. 138 is not a perfect square, so √138 is irrational: its decimals never end or repeat.
| Value | 11.74734012 |
|---|---|
| Rounded | 11.7 (1 dp) · 11.75 (2 dp) · 11.747 (3 dp) |
| Simplest radical form | √138 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 138 squared | 19,044 |
Estimating √138 in your head
Start from the nearest perfect square, 12² = 144. 138 is 6 less than that. Divide the difference by twice the root, 24, and subtract it:
√138 ≈ 12 − 6 ÷ 24 ≈ 11.75
The true value is 11.7473, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 138 is near a perfect square. The method is explained in estimating square roots in your head.
Can √138 be simplified?
No. 138 has no perfect-square factor besides 1, so √138 is already in simplest radical form.
Frequently asked questions
What is the square root of 138?
The square root of 138 is about 11.7473. 138 is not a perfect square, so √138 is irrational: its decimals never end or repeat.
Is 138 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √138 in simplest radical form?
√138 is already in simplest form: 138 has no square factor other than 1.
Practise estimating square rootsNearby: √137 · √139 · all square roots to 150