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

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Answer 1 · 2016-12-28T03:59:19

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

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

= $7/(2sqrt3+2)xx(2sqrt3-2)/(2sqrt3-2)$ 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 $2$

= $(7sqrt3-7)/4$

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