How do you simplify $sqrt(-4/5)$ ?

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Answer 1 · 2015-12-27T14:18:31

$sqrt(-4/5) = i sqrt(4/5) = (2sqrt(5))/5 i$

By definition and convention, if $x < 0$ then $sqrt(x) = i sqrt(-x)$ where $i$ is the imaginary unit.

Also, if $a, b > 0$ then $sqrt(ab) = sqrt(a)sqrt(b)$

So:

$sqrt(-4/5) = i sqrt(4/5) = i sqrt(4/25 * 5) = i sqrt(4/25)sqrt(5) = i sqrt((2/5)^2)sqrt(5)$

$= (2sqrt(5))/5 i$

How do you simplify sqrt(-4/5)sqrt(-4/5)?