Rationalised, $\dfrac{5+\sqrt2}{\sqrt6-\sqrt2}$ simplifies to:

1. Multiply numerator and denominator by the conjugate $\sqrt6+\sqrt2$. 2. The denominator becomes $(\sqrt6)^2-(\sqrt2)^2=6-2=4$. 3. Expand the numerator: $(5+\sqrt2)(\sqrt6+\sqrt2)=5\sqrt6+5\sqrt2+\sqrt{12}+2$. 4. Simplify $\sqrt{12}=2\sqrt3$. 5. So the result is $\dfrac{5\sqrt6+5\sqrt2+2\sqrt3+2}{4}$. Writing the numerator as $30-4$ multiplies the terms instead of expanding them, which the report records as a common slip. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 2: Exponents, Radicals and Logarithms_