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

Question

1365 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-28T00:53:08

I got as far as this:

Multiply and divide by $sqrt(5)+2$ :

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

$=sqrt(10)*[sqrt(5)+2]/(5-4)=sqrt(5*2)*[sqrt(5)+2]/1=$

$=sqrt(5)sqrt(2)*[sqrt(5)+2]=5sqrt(2)+2sqrt(5)sqrt(2)=$

$=sqrt(2)[5+2sqrt(5)]$

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