Question

(6+√25)/(4-√3) can be written in the form of (2+s√3)/13 where r and s are both integers what are the values of r and s

Answer 1

Answer:

r = 33

s = 18

Step-by-step explanation:

Given expression is $\frac{6+\sqrt{27}}{4-\sqrt{3}}$.

Multiply numerator and denominator with the conjugate of (4 - √3).  

$\frac{(6+\sqrt{27})(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}$

= $\frac{4(6+\sqrt{27})+\sqrt{3}(6+\sqrt{27})}{4^{2}-(\sqrt{3})^2}$

= $\frac{24+4\sqrt{27}+6\sqrt{3}+\sqrt{81})}{16-3}$

= $\frac{24+12\sqrt{3}+6\sqrt{3}+\sqrt{81})}{16-3}$

= $\frac{24+18\sqrt{3}+9}{13}$

= $\frac{33+18\sqrt{3}}{13}$

Now compare this expression with $\frac{r+s\sqrt{3} }{13}$

r = 33

s = 18