Question

Simplify square root of -40

Answer 1

Answer: 2i
`√(10)`

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
`√(40)`.

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
`√(10)`.

Answer 2

if you know complex numbers:

sqrt (-40)

sqrt(-1) * sqrt(40)

sqrt(-1) * sqrt(4) * sqrt(10)

i * 2 * sqrt(10)

2i *sqrt(10)

If you do not know complex numbers:

it cannot be simplified because it is negative

no real solution