Question

How do you simplify `-2sqrt15(-3sqrt3+3sqrt5)`?

Answer 1

See a solution process below:

Explanation:

First, multiply each term within the parenthesis by the term outside the parenthesis:

`color(red)(-2sqrt(15))(-3sqrt(3) + 3sqrt(5)) =>`

`(color(red)(-2sqrt(15)) xx -3sqrt(3)) + (color(red)(-2sqrt(15)) xx 3sqrt(5)) =>`

`(color(red)(-2) xx -3)color(red)(sqrt(15))sqrt(3) + (color(red)(-2) xx 3)color(red)(sqrt(15))sqrt(5) =>`

`6sqrt(15 xx 3) + (-6)sqrt(15 xx 5) =>`

`6sqrt(45) - 6sqrt(75)`

Now, we can simplify the radicals:

`6sqrt(45) - 6sqrt(75) =>`

`6sqrt(9 xx 5) - 6sqrt(25 xx 3) =>`

`6sqrt(9)sqrt(5) - 6sqrt(25)sqrt(3) =>`

`(6 * 3)sqrt(5) - (6 * 5)sqrt(3) =>`

`18sqrt(5) - 30sqrt(3)`

Answer 2

`18 sqrt(5) - 30 sqrt(3)`

Explanation:

First, distribute the `-2sqrt(15)`
You end up with:
`6 sqrt(45) - 6 sqrt(75)`
You can then factor under the radical.
`6sqrt(9*5) - 6sqrt(25*5)`
Then, simplify by square rooting the perfect squares.
`6*3 sqrt(5) - 6*5 sqrt(3)`
Then multiply.
`18 sqrt(5) - 30 sqrt(3)`