Square root of 137
√137 ≈ 11.7047. The square root of 137 is about 11.7047. 137 is not a perfect square, so √137 is irrational: its decimals never end or repeat.
| Value | 11.70469991 |
|---|---|
| Rounded | 11.7 (1 dp) · 11.70 (2 dp) · 11.705 (3 dp) |
| Simplest radical form | √137 |
| Perfect square? | No — between 11² = 121 and 12² = 144 |
| 137 squared | 18,769 |
Estimating √137 in your head
Start from the nearest perfect square, 12² = 144. 137 is 7 less than that. Divide the difference by twice the root, 24, and subtract it:
√137 ≈ 12 − 7 ÷ 24 ≈ 11.708
The true value is 11.7047, so the one-step estimate is off by about 0.004. The estimate always comes out slightly high, and it is closest when 137 is near a perfect square. The method is explained in estimating square roots in your head.
Can √137 be simplified?
No. 137 has no perfect-square factor besides 1, so √137 is already in simplest radical form.
Frequently asked questions
What is the square root of 137?
The square root of 137 is about 11.7047. 137 is not a perfect square, so √137 is irrational: its decimals never end or repeat.
Is 137 a perfect square?
No. It lies between 11² = 121 and 12² = 144.
What is √137 in simplest radical form?
√137 is already in simplest form: 137 has no square factor other than 1.
Practise estimating square rootsNearby: √136 · √138 · all square roots to 150