Question

How do you simplify `sqrt(27) - sqrt(8) + 2 sqrt(2)`?

Answer 1

It is

`sqrt(27) - sqrt(8) + 2 sqrt(2)=3*sqrt3-2sqrt2+2sqrt2=3*sqrt3`

Answer 2

`3sqrt(3)`

Explanation:

Since
`color(white)("XXX")color(red)(sqrt(27) = sqrt(3^2*3) = 3sqrt(3))`
and
`color(white)("XXX")color(blue)(sqrt(8) = sqrt(2^2*2) = 2sqrt(2))`

Therefore
`color(white)("XXX")color(red)(sqrt(27)-color(blue)(sqrt(8) + color(green)(2sqrt(2)`

`color(white)("XXX")= color(red)(3sqrt(3))cancel(-color(blue)(2sqrt(2)))cancel(+color(green)(2sqrt(2)))`

`color(white)("XXX")=3sqrt(3)`