Step-by-step explanation:
so when you want to rationalize the denominator when it's in the form [tex](a-\sqrt{b})[/tex] you multiply by the conjugate which is [tex](a+\sqrt{b})[/tex] which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because [tex](a-b)(a+b) = a^2-b^2[/tex] this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root
Multiply by conjugate
[tex]\frac{5\sqrt3}{4-\sqrt6} * \frac{4+\sqrt6}{4+\sqrt6}\\[/tex]
Simplify:
[tex]\frac{20\sqrt{3} + 5\sqrt{6 * 3}}{16-6}[/tex]
Simplify radical
[tex]\frac{20\sqrt{3} + 15\sqrt{2}}{10}\\[/tex]
You could go further and do
[tex]2\sqrt{3} + 1.5\sqrt{2}[/tex]
