Question

rationalise (6-4 root 3)/(6+4 root 3)
$\frac{6 - 4 \sqrt{3 } }{?} \\ 6 + 4 \sqrt{3}$

Answer 1

© 6 - 4√3 / 6 + 4√3

=( 6 - 4√3 ) / (6 + 4√3 ) ×( 6 - 4√3 ) /6 - 4√3)

= ( 6 - 4√3 )^2 / 36 - 48

use identity:-

( a - b )^2= a^2 + b^2 - 2ab

in numerator .

= ( 36 + 48 - 48√3 ) / (- 12)

= 12 ( 3 + 4 - 4 √3 ) / - 12

= - ( 7 - 4 √3 )

= 4√3 - 7

【 hope it helps 】