Question

`5sqrt2-6sqrt2+18sqrt3-15sqrt2-6sqrt3+sqrt3`?

Answer 1

`13sqrt3-16sqrt2`

Explanation:

`color(red)(5sqrt2)-color(red)(6sqrt2)+color(blue)(18sqrt3)-color(red)(15sqrt2)-color(blue)(6sqrt3)+color(blue)(sqrt3)`

Group them accordingly,

`color(blue)(18sqrt3)-color(blue)(6sqrt3)+color(blue)(sqrt3)+color(red)(5sqrt2)-color(red)(6sqrt2)-color(red)(15sqrt2`

Simplify,

`color(blue)(13sqrt3)-color(red)(16sqrt2)`

Answer 2

`16sqrt(2)+13sqrt(13)`

Explanation:

Given: `5sqrt2-6sqrt2+18sqrt3-15sqrt2-6sqrt3+sqrt3`

Group the square root terms:

`[color(white)(2/2)5sqrt(2)-6sqrt(2)-15sqrt(2)color(white)("d")]+[color(white)(2/2)18sqrt(3)-6sqrt(3)+sqrt(3)color(white)("d")]`

Factor out the square roots

`color(white)("d")sqrt(2)[color(white)(2/2)5-6-15color(white)("d")]color(white)("dddd")+color(white)("dd")sqrt(3)[color(white)(2/2)18-6+1color(white)("d")]`

`color(white)("dddd")-sqrt(2)[color(white)(2/2)16color(white)("d")]color(white)("dddddd")+color(white)(dddd"d")sqrt(3)[color(white)(2/2)13color(white)("d")]`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Writing in the conventional format.

`-16sqrt(2)+13sqrt(13)`