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