Question

How do you perform the operation and write the result in standard form given `(3+sqrt(-5))(7-sqrt(-10))`?

Answer 1

`(3+sqrt(-5))(7-sqrt(-10))=(21+5sqrt2)-(3sqrt10+7sqrt5)i`

Explanation:

`(3+sqrt(-5))(7-sqrt(-10))`

= `3×7-3×sqrt(-10)-7sqrt(-5)+sqrt(-5)sqrt(-10)`

= `21-3sqrt((-1)×10)-7sqrt((-1)×5)+sqrt((-5)×(-10))`

= `21-3sqrt10×sqrt(-1)-7sqrt5×sqrt(-1)+sqrt50`

= `(21+sqrt50)-(3sqrt10+7sqrt5)sqrt(-1)`

= `(21+5sqrt2)-(3sqrt10+7sqrt5)i`

as `sqrt(-1)=i`