Question

simplify the following by rationalizing the denominator 6-4√3 by 6+4√3

Answer 1

6-4√3/6+4√3
(6-4√3)/(6+4√3)*(6-4√3)/(6-4√3)
using a2-b2=(a-b) (a+b)
(6-4√3)square/(6)square - (4√3) square
(6)square + (4√3)square - 2(6)(4√3)/36 - 48
36 + 48 - 48√3/ -12
84 - 48√3/-12
12(7-4√3)/-12
-(7-4√3)

 Answer-7+4√3

Answer 2

Answer:

⇒ ( 4√3 - 7 )

Step-by-step explanation:

We have ,

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

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

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

$= > \frac{36 + 48 - 48 \sqrt{3} }{ - 12}$

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

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

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