Question

How do you simplify `sqrt(24x)*sqrt(6x)`?

Answer 1

`12x`

Explanation:

Given: `sqrt(24x)xxsqrt(6x)`

Note that 24 is the same as `4xx6 -> 2^2xx6`

So if we 'split up' the roots we have:

`color(white)("ddddddd")sqrt(2^2)xxsqrt(6)xx sqrt(x)xxsqrt(6)xxsqrt(x)`

Grouping the values:

`color(white)(dddddd"d") sqrt(2^2)xxubrace(sqrt(6)xxsqrt(6))xx ubrace(sqrt(x)xxsqrt(x))`

`color(white)(dddddd"ddd")ubrace(2color(white)("ddddd")xx6color(white)("dddddd")xx x)`

`color(white)(dddddd"ddddddddddd")12x`

Answer 2

`12x`

Explanation:

`sqrt(24x)*sqrt(6x)`

`:.=sqrt(2*2*2*3x)*sqrt(6x)`

`sqrt2*sqrt2=2`

`:.=2sqrt(6x)*sqrt(6x)`

`:.=sqrt6x*sqrt6x=6x`

`:.=2*6x`

`:.=12x`