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

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Answer 1 · 2015-03-31T11:41:23

You first multiply top and bottom with $sqrt5+2$

This will give the special product $A^2-B^2$ as denominator

$=sqrt10/(sqrt5-2)*(sqrt5+2)/(sqrt5+2)$

$=(sqrt(2*5)*sqrt5+2sqrt10)/(sqrt5^2-2^2)$

$=(sqrt(2*5^2)+2sqrt10)/(5-4)$

$=5sqrt2+2sqrt10$

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