Question

How do you simplify `2sqrt5(3+sqrt2)`?

Answer 1

The Distributive Property of Multiplication tells us that `color(blue)(a*(b + c ) = a*b + a* c`

`color(red)(2sqrt5(3+sqrt2)`

`= (2sqrt5)*3+(2sqrt5)*sqrt2`

`= 6sqrt5+2(sqrt5*sqrt2)`

`= 6sqrt5+2(sqrt(5*2))` (Because `color(blue)(sqrta*sqrtb = sqrt(a*b)`

`color(green)(= 6sqrt5+2sqrt(10)`