Which of the following is equivalent to the expression below √( - 169)

Question

Which of the following is equivalent to the expression below
`√( - 169)`

Answer 1

The given expression can be rewritten as

`\sqrt[]{-169}=\sqrt[]{-1*13*13}`

which is equivalent to

`\sqrt[]{-169}=\sqrt[]{-1}*\sqrt[]{13^2}`

By the definition of imaginary number

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

and

`\sqrt[]{13^2}=13`

the answer is:

`\sqrt[]{-169}=13i`

which corresponds to option C