How do you rationalize $5/(sqrt3 +sqrt5)$ ?

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Answer 1 · 2018-03-09T09:57:46

$(5sqrt5+5sqrt3)/(2)$

we are given $5/(sqrt3+sqrt5)$ , to rationalize this multiply both numerator and denominator with $sqrt3-sqrt5$

$5/(sqrt3+sqrt5)$ $*$ $(sqrt3-sqrt5)/(sqrt3-sqrt5)$ now notice that

the denominator resembles $a^2-b^2$ = $(a+b)*(a-b)$

so $(5sqrt3-5sqrt5)/((sqrt3)^2-(sqrt5)^2$

hence, upon simplifying

$(5sqrt3-5sqrt5)/(-2)$

or
$(5sqrt5+5sqrt3)/(2)$

How do you rationalize 5/(sqrt3 +sqrt5)5/(sqrt3 +sqrt5)?