As given by the question,
There are given that the expression
[tex]\sqrt[]{-72}[/tex]
Now,
From the concept of radical rule:
[tex]\sqrt[]{-a}=\sqrt[]{-1}\sqrt[]{a}[/tex]
Then,
Apply the above radical rule into the given function
[tex]\sqrt[]{-72}=\sqrt[]{-1}\sqrt[]{72}[/tex]
Now,
From the concept of imaginary number rule:
[tex]\sqrt[]{-1}=i[/tex]
Then,
Apply the above rule into the given expression
[tex]\begin{gathered} \sqrt[]{-72}=\sqrt[]{-1}\sqrt[]{72} \\ \sqrt[]{-72}=i\sqrt[]{72} \end{gathered}[/tex]
Now,
[tex]\begin{gathered} \sqrt[]{-72}=i\sqrt[]{72} \\ \sqrt[]{-72}=6i\sqrt[]{2} \end{gathered}[/tex]
Hence, the correct option is A.
