Question

How do you simplify `8sqrt(448)`?

Answer 1

`8sqrt(448) = 64sqrt(7)`

Explanation:

Extracting square factors (the only one we really use here is `2^2=4`):

`448 = 2^2xx112`
`color(white)("XX")=2^2*2^2xx28`
`color(white)("XX")=2^2*2^2*2^2xx7`

`rArr`
`sqrt(448) = sqrt(2^2*2^2*2^2*7`
`color(white)("XXX")=(2*2*2)sqrt(7)`
`color(white)("XXX")=8sqrt(7)`

Therefore
`8sqrt(448) = 8*8sqrt(7)`
`color(white)("XXXX")=64sqrt(7)`