We want to simplify the following expression
[tex]\sqrt[]{\text{ -72}}[/tex]
To do so we will use the following properties
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]
and
[tex]\sqrt[]{\text{ -1}}=i[/tex]
So we have that
[tex]\sqrt[]{\text{ -72}}=\sqrt[]{\text{ -1}\cdot72}=\sqrt[]{\text{ -1}}\cdot\sqrt[]{72}=\sqrt[]{72}i=\sqrt[]{8\cdot9}i=\sqrt[]{8}\cdot\sqrt[]{9}i=\pm3\cdot\sqrt[]{8}i=\pm3\cdot\sqrt[]{4\cdot2}i=\pm3\sqrt[]{4}\sqrt[]{2}i[/tex]
which is equal to
[tex]\pm3\cdot2\sqrt[]{2}i=\pm6\sqrt[]{2}i[/tex]
so options A and B are correct
