Answer:
[tex]0+6\sqrt{2}i[/tex]
or just [tex]6\sqrt{2}i[/tex]
Step-by-step explanation:
[tex]\sqrt{-72}[/tex] does not have a real part, it is a pure imaginary number.
Let's simplify.
First step:
[tex]\sqrt{-1}=i[/tex] is the imaginary unit.
So we have that we can write [tex]\sqrt{-72}=i \sqrt{72}[/tex].
Second step:
Let's simplify the factor [tex]\sqrt{72}[/tex] by looking for perfect squares of [tex]72[/tex].
[tex]72=2(36)=2(6^2)[/tex]
So [tex]36[/tex] is a perfect square because it can be written as [tex]6^2[/tex].
[tex]\sqrt{-72}[/tex]
[tex]i \sqrt{72}[/tex]
[tex]i \sqrt{2 \cdot 6^2}[/tex]
[tex]i \sqrt{2} \sqrt{6^2}[/tex]
[tex]i \sqrt{2} 6[/tex]
[tex]6 \sqrt{2}i[/tex]
We could write this as [tex]0+6\sqrt{2}i[/tex].
