Not sure about first question
8√8 = 8(√4 x 2) (you can take the root of 4 out of the bracket)
8 x 2(√2) = 16√2
1/8√8 (to rationalise multiply by √8/√8 to eliminate the √8 from the denominator and so that it is only multiplied by 1 so has to be √8/√8)
1/8√8 x √8/√8 = 1√8/(8 x √8 x √8) = 1√8/(8 x 8) = 1√8/64
which can simplify
1√8/64 = 1(√4 x 2)/64 = 2√2/64