How do you rationalize the denominator and simplify $2/(sqrt6-sqrt5)$ ?

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Answer 1 · 2015-09-24T20:30:34

Refer to explanation

When you have a formula like $sqrta-sqrtb$ in the denominator you multiply with $sqrta+sqrtb$ so

$2/(sqrt6-sqrt5)=2*(sqrt6+sqrt5)/((sqrt6-sqrt5)*(sqrt6+sqrt5))=2*(sqrt6+sqrt5)/((sqrt6)^2-(sqrt5)^2)=2*(sqrt6+sqrt5)/(6-5)=2*(sqrt6+sqrt5)$

Remarks

We used the identity $a^2-b^2=(a-b)*(a+b)$

How do you rationalize the denominator and simplify 2/(sqrt6-sqrt5)2/(sqrt6-sqrt5)?