# Square root

From Maths

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Complex viewpoint would be good, maybe a numerical one for approximating maybe?

## Disambiguation

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**Square root** may refer to:

- Square root (real function) - a map, [ilmath]f:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0} [/ilmath] where [ilmath]f(x)[/ilmath] is typically written [ilmath]\sqrt{x} [/ilmath] or [ilmath]x^\frac{1}{2} [/ilmath]
- Imaginary constant - defined as [ilmath]\sqrt{-1} [/ilmath], typically denoted [ilmath]j[/ilmath] or [ilmath]i[/ilmath] (this site uses [ilmath]j[/ilmath]), this forms the basis of the complex numbers
- Note if we write [ilmath]a+b\sqrt{-1} [/ilmath] we can keep it this way without evaluating [ilmath]\sqrt{-1} [/ilmath], then say we do [ilmath](a+b\sqrt{-1})(c+d\sqrt{-1})[/ilmath] we expand to get [ilmath]ac+bd(\sqrt{-1})^2+\sqrt{-1}(ad+bc)[/ilmath], obviously [ilmath](\sqrt{-1})^2\eq-1[/ilmath] so [ilmath](a+b\sqrt{-1})(c+d\sqrt{-1})\eq ac-bd+\sqrt{-1}(ad+bc)[/ilmath]