Question

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

Answer 1

The expression is equal to `3i`.

Explanation:

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

`sqrt(-9)=3i`

Explanation:

Given:

`sqrt(-9)`

Prime factorize the radicand.

`sqrt(3^2xx-1)`

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

Simplify.

`3i`