Answer:
r = 33
s = 18
Step-by-step explanation:
Given expression is [tex]\frac{6+\sqrt{27}}{4-\sqrt{3}}[/tex].
Multiply numerator and denominator with the conjugate of (4 - √3).
[tex]\frac{(6+\sqrt{27})(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}[/tex]
= [tex]\frac{4(6+\sqrt{27})+\sqrt{3}(6+\sqrt{27})}{4^{2}-(\sqrt{3})^2}[/tex]
= [tex]\frac{24+4\sqrt{27}+6\sqrt{3}+\sqrt{81})}{16-3}[/tex]
= [tex]\frac{24+12\sqrt{3}+6\sqrt{3}+\sqrt{81})}{16-3}[/tex]
= [tex]\frac{24+18\sqrt{3}+9}{13}[/tex]
= [tex]\frac{33+18\sqrt{3}}{13}[/tex]
Now compare this expression with [tex]\frac{r+s\sqrt{3} }{13}[/tex]
r = 33
s = 18
