Question

Simplify the following by rationalising the denominator $\frac{6-4\sqrt{3}}{6+4\sqrt{3}}.$

Answer 1

6​-4√3
6+4√3
By rationalizing above expression
= 6​-4√3 $\times$ 6​-4√3
6+4√3 6​-4√3

$=\frac{6-4\sqrt{3}}{6+4\sqrt{3}}\times \frac{6-4\sqrt{3}}{6-4\sqrt{3}}$

= 36 + 48 - 48√3
​ 36 - 48

= 84 - 48√3
​ -12

= 12(7-4​√3)
-12

= -​7+4​√3
​ ​1


Hence, $\frac{6-4\sqrt{3}}{6+4\sqrt{3}}$= ​4​​√3-7