Question

rationalize the denominator 6 minus 4 root 3 / 6 + 4 root 3

Answer 1

6-4√3/6+4√3

On rationalizing,

=6-4√3×6-4√3/6+4√3×6-4√3

=36+48-48√3/36-48

=84-48√3/-12

=12(7-4√3)/-12

=-(7-4√3)

=4√3-7

Answer 2

Hey, here's your solution,

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

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

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

$= \frac{ {6}^{2} + {4 \sqrt{3} }^{2} - 2(6)(4 \sqrt{3)} }{36 - 48}$

$= \frac{36 + 48 - 12(4 \sqrt{3} )}{ - 12}$

$= \frac{84 - 48 \sqrt{3} }{ - 12}$

$= \frac{12(7 - 4 \sqrt{3}) }{ - 12}$

$= \frac{7 - 4 \sqrt{3} }{ - 1}$

$= \frac{ - ( - 7 + 4 \sqrt{3}) }{ - 1}$

Cancelling minus sign,

$= - 7 + 4 \sqrt{3}$

$= 4 \sqrt{3} - 7$

$\red{Hence, \: amswer\: is \: 4\sqrt{3} -7}$.