Square root of 149
√149 ≈ 12.2066. The square root of 149 is about 12.2066. 149 is not a perfect square, so √149 is irrational: its decimals never end or repeat.
| Value | 12.20655562 |
|---|---|
| Rounded | 12.2 (1 dp) · 12.21 (2 dp) · 12.207 (3 dp) |
| Simplest radical form | √149 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 149 squared | 22,201 |
Estimating √149 in your head
Start from the nearest perfect square, 12² = 144. 149 is 5 more than that. Divide the difference by twice the root, 24, and add it:
√149 ≈ 12 + 5 ÷ 24 ≈ 12.208
The true value is 12.2066, so the one-step estimate is off by about 0.002. The estimate always comes out slightly high, and it is closest when 149 is near a perfect square. The method is explained in estimating square roots in your head.
Can √149 be simplified?
No. 149 has no perfect-square factor besides 1, so √149 is already in simplest radical form.
Frequently asked questions
What is the square root of 149?
The square root of 149 is about 12.2066. 149 is not a perfect square, so √149 is irrational: its decimals never end or repeat.
Is 149 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √149 in simplest radical form?
√149 is already in simplest form: 149 has no square factor other than 1.
Practise estimating square rootsNearby: √148 · √150 · all square roots to 150