Square root of 146
√146 ≈ 12.083. The square root of 146 is about 12.083. 146 is not a perfect square, so √146 is irrational: its decimals never end or repeat.
| Value | 12.08304597 |
|---|---|
| Rounded | 12.1 (1 dp) · 12.08 (2 dp) · 12.083 (3 dp) |
| Simplest radical form | √146 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 146 squared | 21,316 |
Estimating √146 in your head
Start from the nearest perfect square, 12² = 144. 146 is 2 more than that. Divide the difference by twice the root, 24, and add it:
√146 ≈ 12 + 2 ÷ 24 ≈ 12.083
The true value is 12.083, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 146 is near a perfect square. The method is explained in estimating square roots in your head.
Can √146 be simplified?
No. 146 has no perfect-square factor besides 1, so √146 is already in simplest radical form.
Frequently asked questions
What is the square root of 146?
The square root of 146 is about 12.083. 146 is not a perfect square, so √146 is irrational: its decimals never end or repeat.
Is 146 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √146 in simplest radical form?
√146 is already in simplest form: 146 has no square factor other than 1.
Practise estimating square rootsNearby: √145 · √147 · all square roots to 150