How do you simplify Square root of (-16/25)??

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Answer 1 · 2018-03-11T07:34:58

The expression is equal to $(4i)/5$ .

Use these properties of radicals:

$sqrt(color(red)a/color(blue)b)=sqrtcolor(red)a/sqrtcolor(blue)b$

$sqrt(color(red)a^2)=color(red)a$

$sqrt(color(red)a^2*color(blue)b)=color(red)asqrtcolor(blue)b$

$sqrt(-1)=i$

Now here's the actual expression:

$color(white)=sqrt(-16/25)$

$=sqrt((-16)/25)$

$=sqrt(-16)/sqrt25$

$=sqrt(4*4*-1)/sqrt(5*5)$

$=sqrt(4^2*-1)/sqrt(5^2)$

$=(4sqrt(-1))/5$

$=(4i)/5$