The square root of 12 is not a rational number. To understand why, we first need to define what a rational number is. A rational number can be expressed as the quotient or fraction a/b, where a and b are integers and b is not zero.
Now, let’s simplify the square root of 12. The square root can be broken down as follows:
√12 = √(4 × 3) = √4 × √3 = 2√3
Here, √3 is an important part of our answer. The square root of 3 is an irrational number, meaning it cannot be expressed as a fraction of two integers. Therefore, when we multiply 2 (a rational number) by √3 (an irrational number), the result is still irrational.
Thus, since the square root of 12 can be simplified to 2√3, which is irrational, we can conclude that the square root of 12 is not a rational number.