Computing (or computing with) a square root is much easier than solving a quadratic equation!
- A square root’s result is always nonnegative (or in the complex case, has nonnegative real part) and unique, whereas the quadratic equation has two solutions.
- You can manipulate the root function symbolically much better than the roots of an equation. sqrt(2)^2 is 2, but figuring out that `solution(x^2-2=0)^2` reduces to the same number is much less obvious, and even more so for more complicated roots.
>A square root’s result is always nonnegative (or in the complex case, has nonnegative real part)
I don’t know what definition you’re using, but if we take the square root of Y to be a number X such that X*X = Y, then the above statement isn’t true.
The principal square root (ie, the one with positive part) is commonly referred to as the square root, especially since the radical symbol is explicitly defined to produce the principal root.
- A square root’s result is always nonnegative (or in the complex case, has nonnegative real part) and unique, whereas the quadratic equation has two solutions.
- You can manipulate the root function symbolically much better than the roots of an equation. sqrt(2)^2 is 2, but figuring out that `solution(x^2-2=0)^2` reduces to the same number is much less obvious, and even more so for more complicated roots.