Question

How do you simplify `5sqrt3(6sqrt10-6sqrt3)`?

Answer 1

`30(sqrt30-3)`

Explanation:

We essentially have the following

`color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt10)-color(blue)(5)color(lime)(sqrt3)*color(blue)(6)color(lime)(sqrt3)`

Which can be simplified if we multiply the integers and square roots together, respectively. We'll get

`color(blue)((5*6))color(lime)(sqrt3sqrt10)-color(blue)((5*6))color(lime)(sqrt3sqrt3)`

Which simplifies to

`color(blue)(30)color(lime)(sqrt30)-color(blue)(30)*color(lime)(3)`

`=>color(blue)(30)color(lime)(sqrt30)-90`

Since `30` has no perfect square factors, we cannot simplify the radical any further. We can factor a `30` out of both terms, however. We get

`30(sqrt30-3)`

Hope this helps!