Question

Simplify: ✓- 72 O A - 6iva O B. 6iv 2 O c. 5i/3 OD. – 517 3

Answer 1

We want to simplify the following expression

`\sqrt[]{\text{ -72}}`

To do so we will use the following properties

`\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}`

and

`\sqrt[]{\text{ -1}}=i`

So we have that

`\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`

which is equal to

`\pm3\cdot2\sqrt[]{2}i=\pm6\sqrt[]{2}i`

so options A and B are correct