What is the $\sqrt{- 25}$ $sqrt(-25)$ ?

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What is the $\sqrt{- 25}$ $sqrt(-25)$ ?

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Answer 1 · 2016-08-14T21:27:43

$\sqrt{- 25} = 5 i$ $sqrt(-25) = 5i$

Explanation:

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

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

$\sqrt{- 25} = (\sqrt{25}) i = (\sqrt{5^{2}}) i = 5 i$ $sqrt(-25) = (sqrt(25))i = (sqrt(5^2))i = 5i$

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What is the $\sqrt{- 25}$ $sqrt(-25)$ ?

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