Question

How do you simplify `12-15sqrt6 + 8sqrt6 - 10sqrt36`?

Answer 1

`-48-7sqrt(6)`

Explanation:

`12-15sqrt(6)+8sqrt(6)-10sqrt(36)`
`=12-15sqrt(6)+8sqrt(6)-10sqrt(6^2)`
`=12-15sqrt(6)+8sqrt(6)-10*6`
`=12-15sqrt(6)+8sqrt(6)-60`
`=12-60+(-15+8)sqrt(6)`
`=-48-7sqrt(6)`

Answer 2

`-48-(7*sqrt(6))`

Explanation:

`12+(-15*sqrt(6))+(8*sqrt(6))+(-10*sqrt(36))`

We know that `sqrt(36)=6`.

So, `12+(-15sqrt(6))+(8*sqrt(6))+(-60)`.

`12-60=-48`

So, `-48+(-15sqrt(6))+(8*sqrt(6))`

Now, take out `sqrt(6)` from last two parenthesis.

That would give us `-48+(sqrt(6)*(-15+8))`

`-15+8=-7`

So, the answer would be `-48-(7*sqrt(6))`