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

1 Answer
Mar 11, 2018

Answer:

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

Explanation:

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#