Question

(6 + root27)/(4 - root3) can be written in the form (r + sroot3)/13

Answer 1

Answer:

r = 33 , s = 18

Step-by-step explanation:

Rationalise the denominator by multiplying both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 - $\sqrt{3}$ is 4 + $\sqrt{3}$ , then

$\frac{(6+\sqrt{27})(4+\sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3}) }$ ← expand numerator/denominator using FOIL

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

= $\frac{24+6\sqrt{3}+4(3\sqrt{3}+9 }{16-3}$

= $\frac{33+6\sqrt{3}+12\sqrt{3} }{13}$

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

with r = 33 and s = 18