Square root of 148
√148 ≈ 12.1655. The square root of 148 is about 12.1655, which simplifies to 2√37. 148 is not a perfect square, so √148 is irrational: its decimals never end or repeat.
| Value | 12.16552506 |
|---|---|
| Rounded | 12.2 (1 dp) · 12.17 (2 dp) · 12.166 (3 dp) |
| Simplest radical form | 2√37 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 148 squared | 21,904 |
Estimating √148 in your head
Start from the nearest perfect square, 12² = 144. 148 is 4 more than that. Divide the difference by twice the root, 24, and add it:
√148 ≈ 12 + 4 ÷ 24 ≈ 12.167
The true value is 12.1655, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 148 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √148
Find the largest perfect square that divides 148: it is 4, since 148 = 4 × 37. Take its root outside: √148 = √4 × √37 = 2√37.
Frequently asked questions
What is the square root of 148?
The square root of 148 is about 12.1655, which simplifies to 2√37. 148 is not a perfect square, so √148 is irrational: its decimals never end or repeat.
Is 148 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √148 in simplest radical form?
√148 = √(4 × 37) = 2√37.
Practise estimating square rootsNearby: √147 · √149 · all square roots to 150