Question

What is the simplest radical form of `-2sqrt96`?

Answer 1

`-2sqrt(96) = -8sqrt(6)`

Explanation:

Factoring `96`
`color(white)("XXXX")` `=2xx48`
`color(white)("XXXX")` `=2^2xx24`
`color(white)("XXXX")` `=2^2xx2xx12`
`color(white)("XXXX")` `=2^2xx2^2xx6`
`color(white)("XXXX")` `=2^2xx2^2xx2xx3`

`sqrt(96)`
`color(white)("XXXX")` `= sqrt(2^2xx2^2xx2xx3)`
`color(white)("XXXX")` `=sqrt(2^2)xxsqrt(2^2) xxsqrt(2xx3)`
`color(white)("XXXX")` `=2xx2xxsqrt(6)`
`color(white)("XXXX")` `=4sqrt(6)`

`-2sqrt(96)`
`color(white)("XXXX")` `=(-2)xx(4sqrt(6))`
`color(white)("XXXX")` `=-8sqrt(6)`