Question

Simplify the following expression: square root of -36 + square root of -100 +7

Answer 1

`\large\boxed{√(-36)+√(-100)+7=7+16i}`

Explanation:

`√(-1)=i\\√(ab)=√(a)\cdot√(b)\\=====================\\\\√(-36)=√((36)(-1))=√(36)\cdot\sqrT{-1}=6i\\√(-100)=√((100)(-1))=√(100)\cdot√(-1)=10i\\\\√(-36)+√(-100)+7=6i+10i+7=7+16i`

Answer 2

The answer is
`16i+7`

Explanation:

In order to determine the answer, we have to know about imaginary numbers.

The imaginary numbers are different to real numbers because they use a new unit called "imaginary unit":

`i=√(-1)`

i: imaginary unit

This new unit is applied like a factor when we have even roots with negative numbers inside.

In this case:

`√(-36)=√(-1)*√(36)=6i\\√(-100)=√(-1)*√(100)=10i\\   \\√(-36)+√(-100)+7\\ 6i+10i+7\\16i+7`

Finally, the answer is
`16i+7`