The square root of a number is a value that, when multiplied by itself, gives the original number. When we talk about the square root of x2, we are looking for a value that, when squared, results in x2.
Mathematically, the square root of x2 can be expressed as:
√(x2) = x
However, this is true under the assumption that x is a non-negative number. In mathematical terms, we often consider the principal square root, which is the non-negative value. Therefore, for any x ≥ 0, the square root of x2 would simply be x.
On the other hand, if x could also be negative, we’d need to state that:
√(x2) = |x|
Where |x| denotes the absolute value of x. This notation clarifies that whether x is positive or negative, the square root will yield a non-negative result.
In summary, the square root of x2 can be represented as follows:
- If x ≥ 0: √(x2) = x
- If x < 0: √(x2) = -x
- General case: √(x2) = |x|