How do you simplify `(2sqrt27)times(3 sqrt32)`?

`(color(blue)2sqrt(color(green)(27))) xx (color(red)3sqrt(color(magenta)(32)))`

`color(white)("XXX")=color(blue)2xxcolor(red)3xxsqrt(color(green)(3^3))xxsqrt(color(magenta)(2^5))`

`color(white)("XXX")=6 xx color(green)3sqrt(color(green)3)xxcolor(magenta)(2^2)sqrt(color(magenta)2)`

`color(white)("XXX")=6xxcolor(green)3xxcolor(magenta)(2^2)xxsqrt(color(green)3xxcolor(magenta)2)`

`color(white)("XXX")=72sqrt(6)`

Using the `color(blue)"law of radicals"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(sqrt(ab)hArrsqrtaxxsqrtb)color(white)(2/2)|)))`

To simplify the radicals consider the product of their factors of which one should be a `color(blue)"perfect square"`

`rArrsqrt27=sqrt(color(red)(9)xx3)=sqrtcolor(red)(9)xxsqrt3=3sqrt3`

`rArrsqrt32=sqrt(color(red)(16)xx2)=sqrtcolor(red)(16)xxsqrt2=4sqrt2`

`rArr2sqrt27xx3sqrt32`

`=2xx(3xxsqrt3)xx3xx(4xxsqrt2)`

`=(2xx3xx3xx4)xx(sqrt3xxsqrt2)`

`=72sqrt(3xx2)=72sqrt6`

`(2sqrt27) xx (3sqrt32)`

`:.=2sqrt(3*3*3) xx 3sqrt(2*2*2*2*2)`

`:.=2 xx 3sqrt3 xx 3*2*2sqrt2`

`:.=6sqrt3 xx 12sqrt2`

`:.=72sqrt3sqrt2`

`:.=72sqrt(2*3)`

`:.=72sqrt6`