Question

How do you evaluate `\frac { 7} { 2+ 2\sqrt { 3} }`?

Answer 1

`7/(2+2sqrt3)=(7sqrt3-7)/4`

Explanation:

`7/(2+2sqrt3)=7/(2sqrt3+2)`

= `7/(2sqrt3+2)xx(2sqrt3-2)/(2sqrt3-2)` and using `(a+b)(a-b)=(a^2-b^2)`, we get

`(7(2sqrt3-2))/((2sqrt3)^2-2^2)`

= `(14sqrt3-14)/(12-4)`

= `(14sqrt3-14)/8` and dividing numerator and denominator by `2`

= `(7sqrt3-7)/4`