Question

How do you simplify `5sqrt(-75 )+ 3sqrt(-48)`?

Answer 1

`37 sqrt3 i`

Explanation:

Consider the factors of (- 75 ) and )- 48 )

factors of ( - 75 ) = 25 `xx 3 xx ( - 1 )`

factors of ( - 48 ) = 16 `xx 3 xx( - 1 )`

`rArr 5sqrt-75 = 5sqrt25 sqrt3sqrt-1 = 5. 5 .sqrt3 . i = 25sqrt3 i`

and `3sqrt-48 = 3sqrt16sqrt3sqrt-1 = 3 . 4 .sqrt3 . i = 12sqrt3 i`

`rArr 5sqrt-75 + 3sqrt-48 = 25sqrt3 i + 12sqrt3 i = 37sqrt3 i`