Square Root of 12
The square root of 12 is about 3.4641. Square roots reverse squaring and are essential in geometry and the quadratic formula.
√12 is irrational — 12 sits between the squares 9 and 16, and no whole number between their roots can multiply by itself to give 12, so the decimal never ends nor repeats. The nearer fence sits 3 away, against 4 on the other side. Rounded to two places, 3.46 misses the true value by less than one hundredth. Slanted right-triangle sides and the quadratic formula both land on roots of exactly this kind. No fraction of integers nails it either: if a ratio a/b squared gave 12, then 12 would itself be a perfect square — which the ladder above shows it is not. That property has a name, irrationality, and it is a fact about the number, not a limit of this table.
| Expression | Value |
|---|---|
| √12 | 3.464102 |
Frequently asked questions
What is the square root of 12?
The square root of 12 is about 3.4641. It is the number that, multiplied by itself, gives 12.
Is 12 a perfect square?
No — 12 sits between the perfect squares 9 and 16, so its square root is irrational.
What does √ mean?
√ is the radical sign, short for square root. √12 asks: which number times itself equals 12? Here the answer is about 3.4641.