Question

Simply 6-4 root 3/ 6+4 root 3 by ratnolising the denominator

Answer 1

-7+4√3.

Explanation:

6-4√3 / 6+4√3 Multiply top and bottom by 6-4√3:-

= (6-4√3)( 6-4√3) / (6+4√3)(6- 4√3)

= (36-24√3- 24√3+48) / (36-48)

= (36-48√3+48) / (-12)

= -3 +4√3 - 4

= -7 + 4√3.

Answer 2

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

the question asks us to rationalise the given expression !

so let's start ~

`(6 - 4 √(3) )/(6 + 4 √(3) ) \\ \\ \implies \: (6 - 4 √(3) )/(6 + 4 √(3) ) \: * \: (6 - 4 √(3) )/(6 - 4 √(3) ) = \frac{(6 - 4 √(3)) {}^(2) }{6 {}^(2) - 4 √(3) {}^(2) } \\ \\ \implies \frac{\: 6 {}^(2) + 4 √(3) {}^(2) - (2 * 6 * 4 √(3) )}{36 - 48} \\ \\ \implies \: (36 + 48 - 48 √(3) )/( - 12) \\ \\ \implies \: (84 + 48 √(3) )/( - 12) \\ \\ \implies \: \frac{ \cancel{- 12}(7 - 4 √(3) )}{ \cancel{ - 12} } \\ \\ \implies \: 7 - 4 √(3)`

hope helpful :D