Answer: 2i [tex]\sqrt{10}[/tex]
Step-by-step explanation: To simplify the square root of -40, think of the square root of -40 as the square root of -1 × the square root of 40.
The square root of -1 can be represented by the imaginary number i. So we have i × the square root of 40 or i [tex]\sqrt{40}[/tex].
Next, root 40 breaks down breaks down to 2 root 10. We can see this by setting up a factor tree for 40. 40 is 2 x 20, 20 is 2 x 10, and 10 is 2 x 5. We have a pair of 2's in our factor tree and we have 2 x 5 at the bottom.
So we have i x 2 root 10 or 2i [tex]\sqrt{10}[/tex].
