Question

How do you simplify `(-5sqrt6)(2sqrt3)`?

Answer 1

`(-5sqrt6)(2sqrt3)=-30sqrt2`

Explanation:

`(-5sqrt6)(2sqrt3)`

= `(-5)xxsqrt6xx2xxsqrt3`

= `-(5xx2xxsqrt6xxsqrt3)`

= `-(10xxsqrt(6xx3))`

= `-(10xxsqrt(2xxul(3xx3)))`

= `-10xx3xxsqrt2`

= `-30sqrt2`

Answer 2

`-30sqrt2`

Explanation:

This is all one term made of factors multiplied together.

`color(white)(.........)-5 xxcolor(blue)(sqrt6) xx2xxsqrt3`
`color(white)(......................)darr`
`=-5 xxcolor(blue)(sqrt2xxsqrt3)xx2xxsqrt3" "larr` now re-arrange

`= color(green)(-5 xx2) xxcolor(red)(sqrt3 xxsqrt3) xxsqrt2`

`= color(green)(-10) xxcolor(red)(3) xxsqrt2`

`=-30sqrt2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Remember that:

`color(red)(sqrt3 xxsqrt3 = color(red)(sqrt3)^2 = 3)`