Question

How do you simplify `9 sqrt 2 (2 sqrt 7 + 5 sqrt 5)`?

Answer 1

`18sqrt(14)+45sqrt(10)`

Explanation:

`1`. Distribute the `color(blue)9color(red)(sqrt(2))` to each term within the brackets.

`color(red)9color(blue)(sqrt(2))(color(orange)2color(purple)(sqrt(7))+color(teal)5color(brown)(sqrt(5)))`

`=(color(red)9xxcolor(orange)2)sqrt(color(blue)2xxcolor(purple)7)+(color(red)9xxcolor(teal)5)sqrt(color(blue)2xxcolor(brown)5)`

`2`. Simplify.

`=color(green)(|bar(ul(color(white)(a/a)18sqrt(14)+45sqrt(10)color(white)(a/a)|)))`