Find the simplest rationalising factor
\[ 2\sqrt{5} – \sqrt{3} \]
Solution:
\[ \text{Rationalising factor of } (a – b) = (a + b) \]
\[ \therefore \text{Rationalising factor of } (2\sqrt{5} – \sqrt{3}) = 2\sqrt{5} + \sqrt{3} \]
\[ (2\sqrt{5} – \sqrt{3})(2\sqrt{5} + \sqrt{3}) = 20 – 3 = 17 \ (\text{rational}) \]
\[ \therefore \text{Correct Answer: } 2\sqrt{5} + \sqrt{3} \ (\text{Option b}) \]