Question

Express sqroot - 72 in its simplest form. O A. 6iv 2 B. 2iv 18 O c. 3iv 8 c O D. Cannot be determined

Answer 1

As given by the question,

There are given that the expression

`\sqrt[]{-72}`

Now,

From the concept of radical rule:

`\sqrt[]{-a}=\sqrt[]{-1}\sqrt[]{a}`

Then,

Apply the above radical rule into the given function

`\sqrt[]{-72}=\sqrt[]{-1}\sqrt[]{72}`

Now,

From the concept of imaginary number rule:

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

Then,

Apply the above rule into the given expression

`\begin{gathered} \sqrt[]{-72}=\sqrt[]{-1}\sqrt[]{72} \\ \sqrt[]{-72}=i\sqrt[]{72} \end{gathered}`

Now,

`\begin{gathered} \sqrt[]{-72}=i\sqrt[]{72} \\ \sqrt[]{-72}=6i\sqrt[]{2} \end{gathered}`

Hence, the correct option is A.