# What is the square root of #144-x^2#?

##### 1 Answer

By definition, a square root of any number is a number which, if multiplied by itself, produces an original number.

If just a sign of a square root is used, like

If we want both positive and negative square roots, it's customary to use

If it's not a number to take a square root of, but an algebraic expression, you might or might not come up with another simpler algebraic expression that, if squared, produces the original expression. For instance, you can equate

(notice the absolute value because, as we indicated above, a sign of a square root traditionally implies the non-negative value only).

In a particular case of this problem there is no simpler algebraic expression of a square root rather than

The fact that

In addition, it should be noted that this expression is usually considered within a domain of *real* numbers (unless specifically indicated that it's within a domain of *complex* numbers). This implies a restriction for

Only if *real* numbers.