How do you rationalize the denominator and simplify $5/(sqrt3+sqrt5)$ ?

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Answer 1 · 2017-06-04T17:10:32

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

If you have a denominator of type $sqrta+sqrtb$ , to rationalize multiply numerator and denominator by $sqrta-sqrtb$ or vice-versa.

Hence to rationalize $5/(sqrt3+sqrt5)$ multiply numerator and denominator by $sqrt3-sqrt5$ and you get

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

= $(5sqrt3-5sqrt5)/(3-5)$

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

= $5sqrt5-5sqrt3)/2$

How do you rationalize the denominator and simplify 5/(sqrt3+sqrt5)5/(sqrt3+sqrt5)?