Question

How to solve this problem

Answer 1

Answer:

Solving the radical $\pm\sqrt{-81}$  we get $\mathbf{\pm9 \ i}$

Step-by-step explanation:

We need to express the radical $\pm\sqrt{-81}$ using the imaginary unit i

Prime factors of 81 are: 3x3x3x3

and $\sqrt{-1}=i$

Solving:

$\pm\sqrt{-81}\\=\pm\sqrt{81}\sqrt{-1}\\=\pm\sqrt{3\times3\times3\times3}i\\ =\pm\sqrt{3^2\times3^2}i\\=\pm3\times3\ i\\=\pm9 \ i$

So, Solving the radical $\pm\sqrt{-81}$  we get $\mathbf{\pm9 \ i}$