Question

How do you simplify `3 (sqrt 48)-12 (sqrt 75) + 4 (sqrt 12)`?

Answer 1

`3sqrt(48)-12sqrt(75)+4sqrt(12)=color(brown)(-40sqrt(3)`

Explanation:

`48 = 4^2*sqrt(3)`
`color(white)("XXXXXXXX")rarr color(red)(3sqrt(48)=color(white)("XXX")12sqrt(3))`
`75= 5^2*3`
`color(white)("XXXXXXXX")rarr color(blue)(-12sqrt(75)=-60sqrt(3)`
`12=2^2*3`
`color(white)("XXXXXXXX")rarr color(green)(4sqrt(12)=color(white)("XXXX")underline(8sqrt(3)))`

`rArr color(red)(3sqrt(48))color(blue)(-12sqrt(75))+color(green)(4sqrt(12)) = -40sqrt(3)`