How do you rationalize the denominator and simplify $sqrt3/(2+sqrt2)$ ?

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Answer 1 · 2016-12-18T23:12:39

You multiply by $1$ , disguised as $(2-sqrt2)/(2-sqrt2)$

$=(sqrt3xx(2-sqrt2))/((2+sqrt2)xx(2-sqrt2))$

The denominator is now a special product of the sort:
$(A+B)(A-B)=A^2-B^2$

$=(sqrt3xx(2-sqrt2))/(2^2-sqrt2^2)=(2sqrt3-sqrt2*sqrt3)/(4-2)$

$=(2sqrt3-sqrt6)/2=sqrt3-1/2sqrt6$

How do you rationalize the denominator and simplify sqrt3/(2+sqrt2)sqrt3/(2+sqrt2)?