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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
by quchen 4y ago
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.
- comte7092 4y ago>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.
- Armisael16 4y agoThe 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.
- comte7092 4y agoIt just seems odd, because the reason why the quadratic equation has/can have two solutions, is due directly to the square root having two solutions.