Simplify square root of negative 48

Question

marissalovescats · Answer

Hi and welcome to OpenStudy! 

As you know, 48 is not a perfect square, so we want to find the largest perfect square that divides evenly into 48. 

Perfect squares: 

1,4,9,16,25,etc 

So which one is the largest that evenly goes into 48?

marissalovescats · Answer

If you answer 16, you're correct. 16*3=48 so now under the radical we have this: 

$$\sqrt{16*3}$$

But you ask how do we make i negative? If you recall, i^2=-1 so we do 16*i^2 would be teh same as 16*-1: 

$$\sqrt{16*i^2*3}$$

And we know the square root of 16 is 4, and the square root of i^2 is i. So now we have out final answer: $$4i \sqrt{3}$$

acxbox22 · Answer

$\Huge\color{green}{\bigstar}\Huge\color{green}{\bigstar}\huge\color{blue}{WELCOME~TO~OPEN~STUDY}\Huge\color{orange}{\bigstar}\Huge\color{orange}{\bigstar}$

marissalovescats · Answer

That's really cool lol

acxbox22 · Answer

are you looking for real roots or imaginary roots?

acxbox22 · Answer

if real then there are no real solutions to the sqrt of -48

acxbox22 · Answer

thx @marissalovescats

marissalovescats · Answer

Yes no real ones, but imaginary ones as I put