Explanation:
I assume you mean we need to simplify this.
(6 - sqrt(32 - 6))/6 =
= 6/6 - sqrt(32 - 6)/6 =
= 1 - sqrt((32 - 6)/36)
remember, if we want to bring a factor of 6 or 1/6 into a square root expression (radical), we need to square it first to 36 or 1/36.
1 - sqrt((32 - 6)/36) =
= 1 - sqrt(32/36 - 6/36) =
= 1 - sqrt(8/9 - 1/6)
now, let's bring both fractions inside the square root to the same denominator (= smallest common multiple = 18 for 9 and 6).
1 - sqrt(8/9 - 1/6) =
= 1 - sqrt(16/18 - 3/18) =
= 1 - sqrt(13/18) = 1 - sqrt(13/(2×9)) =
= 1 - sqrt(13/2)/3
that's it. there is nothing else we could do.
I personally would use the last but one line
1 - sqrt(13/18)
but it depends what your teacher wants to see.
so, please choose the last but one or the last line depending on your teacher's preferences (see your class notes).