How do you simplify #sqrt(-9)#?

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Answer 1 · 2018-03-25T23:37:25

The expression is equal to #3i#.

Remember these two radical rules:

#sqrt(color(red)acolor(blue)b)=sqrtcolor(red)a*sqrtcolor(blue)b#

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

And also the definition of the imaginary number:

#sqrt(-1)=i#

Here are these properties applied to our expression.

#color(white)=sqrt(-9)#

#=sqrt(-3*3)#

#=sqrt(-1*3*3)#

#=sqrt(-1*3^2)#

#=sqrt(-1)*sqrt(3^2)#

#=sqrt(-1)*3#

#=i*3#

#=3i#

This is the result. Hope this helped!

Answer 2 · 2018-03-25T23:43:22

#sqrt(-9)=3i#

Given:

#sqrt(-9)#

Prime factorize the radicand.

#sqrt(3^2xx-1)#

Apply rule: #sqrt(a^2)=a#, and #sqrt(-1)=i#.

Simplify.

#3i#