The rationalising factor needed to simplify $\dfrac{5+\sqrt2}{\sqrt6-\sqrt2}$ is:

1. Rationalising removes the radicals from the denominator. 2. The denominator is $\sqrt6-\sqrt2$, so multiply above and below by its conjugate. 3. The conjugate flips the middle sign, giving $\sqrt6+\sqrt2$. 4. Then $(\sqrt6-\sqrt2)(\sqrt6+\sqrt2)=6-2=4$, which is rational. 5. Using $\sqrt6-\sqrt2$ again, a recorded error, leaves a radical behind instead of clearing it. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 2: Exponents, Radicals and Logarithms_