What is the $sqrt(-25)$ ?

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Answer 1 · 2016-08-14T21:27:43

$sqrt(-25) = 5i$

$-25$ has two square roots $5i$ and $-5i$ , but the expression $sqrt(-25)$ denotes the principal square root, which by convention is $5i$ .

In general, if $x < 0$ then $sqrt(x) = (sqrt(-x))i$ . Hence in our example:

$sqrt(-25) = (sqrt(25))i = (sqrt(5^2))i = 5i$

What is the sqrt(-25)sqrt(-25)?