Answer:
[tex]6i\sqrt{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{-72}[/tex]
Rewrite -72 as the product of 6 · -1 · 2:
[tex]\implies \sqrt{36 \cdot -1 \cdot 2}[/tex]
Apply the radical rule [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36} \sqrt{-1} \sqrt{2}[/tex]
Carry out the square root of 36:
[tex]\implies 6\sqrt{-1}\sqrt{2}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex] :
[tex]\implies 6i\sqrt{2}[/tex]
