How do you simplify #(sqrt5+2sqrt2)/(4-sqrt5)#?

1 Answer
Jan 15, 2017

Answer:

Use the conjugate of the denominator to turn it into a whole number. Details below...

Explanation:

The first thing you want to do is eliminate the radical expression in the denominator. To do this, multiply top and bottom by the conjugate of the denominator, namely #4+sqrt5#

#((sqrt5 + 2sqrt2)(4+sqrt5))/((4-sqrt5)(4+sqrt5)) #

Use the FOIL method to multiply top and bottom

#(4sqrt5+5+8sqrt2+2sqrt10)/(16-5)#

#(4sqrt5+5+8sqrt2+2sqrt10)/11#

I think that is all you can do!