Given 8−3√62√3+3√2,
first, we rationalise by multiplying through with 2√3−3√2 (the inverse of the denominator).
(8−3√62√3+3√2)(2√3−3√22√3−3√2)
= 16√3−24√2−18√2+18√34(3)−6√6+6√6−9(2)
= 34√3−42√2−6=7√2−17√33