Square root of 12
√12 ≈ 3.4641. The square root of 12 is about 3.4641, which simplifies to 2√3. 12 is not a perfect square, so √12 is irrational: its decimals never end or repeat.
| Value | 3.46410162 |
|---|---|
| Rounded | 3.5 (1 dp) · 3.46 (2 dp) · 3.464 (3 dp) |
| Simplest radical form | 2√3 |
| Perfect square? | No — between 3² = 9 and 4² = 16 |
| 12 squared | 144 |
Estimating √12 in your head
Start from the nearest perfect square, 3² = 9. 12 is 3 more than that. Divide the difference by twice the root, 6, and add it:
√12 ≈ 3 + 3 ÷ 6 ≈ 3.5
The true value is 3.4641, so the one-step estimate is off by about 0.036. The estimate always comes out slightly high, and it is closest when 12 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √12
Find the largest perfect square that divides 12: it is 4, since 12 = 4 × 3. Take its root outside: √12 = √4 × √3 = 2√3.
Frequently asked questions
What is the square root of 12?
The square root of 12 is about 3.4641, which simplifies to 2√3. 12 is not a perfect square, so √12 is irrational: its decimals never end or repeat.
Is 12 a perfect square?
No. It lies between 3² = 9 and 4² = 16.
What is √12 in simplest radical form?
√12 = √(4 × 3) = 2√3.
Practise estimating square rootsNearby: √11 · √13 · all square roots to 150