How do you rationalize the denominator and simplify $sqrt(10)/(sqrt(5)-2)$ ?

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Answer 1 · 2015-04-01T02:39:58

Multiply the numerator and the denominator by the conjugate of the denominator:

$sqrt(10)/(sqrt(5) - 2)$

$= sqrt(10)/(sqrt(5)-2) * (sqrt(5)+2)/(sqrt(5)+2)$

$= (sqrt(10)*sqrt(5)+2sqrt(10))/(5-4)$

$= 5sqrt(2) + 2sqrt(10)$

How do you rationalize the denominator and simplify sqrt(10)/(sqrt(5)-2)sqrt(10)/(sqrt(5)-2)?