What is the square root of this equation?

${x}^{2}$=-16

Apr 14, 2017

$x = \pm 4 i$

Explanation:

Given:

${x}^{2} = - 16$

We might say that to solve the equation you should take the square root, which essentially means take the square root of both sides of the equation. The problem with such a statement is that under normal circumstances any non-zero number has two square roots. Those roots may be real or non-real complex roots, but one is minus the other.

In our example we find:

$x = \pm 4 i$

where ${i}^{2} = - 1$

That is:

$x = 4 i \text{ }$ or $\text{ } x = - 4 i$

So you could say that "the square root of the equation" is the disjunction:

$x = 4 i \vee x = - 4 i$

which we abbreviate to:

$x = \pm 4 i$