Question

How do you simplify `-8sqrt(384)`?

Answer 1

`-8sqrt(384) = -64sqrt(6)`

Explanation:

`384`
`color(white)("XXXX")` `=2*192`
`color(white)("XXXX")` `=2^2*96`
`color(white)("XXXX")` `=2^3*48`
`color(white)("XXXX")` `=2^4*24`
`color(white)("XXXX")` `=2^5*12`
`color(white)("XXXX")` `=2^6*6`
`color(white)("XXXX")` `=2^7*3`

`color(white)("XXXX")` `=(2^3)^2 * 2^1*3`
`color(white)("XXXX")` `= 8^2*6`

`-8sqrt(384)`
`color(white)("XXXX")` `= (-8)*8sqrt(6)`
`color(white)("XXXX")` `=-64sqrt(6)`