How do you rationalize the denominator and simplify #(1+sqrt5)/(10+4sqrt15)#?

Question

1742 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-12T15:53:33

#frac{-5 + 2 sqrt 15 - 5 sqrt 5 + 10 sqrt 3}{70}#

#frac{1 + sqrt 5}{10 + 4 sqrt 15} * frac{10 - 4 sqrt 15}{10 - 4 sqrt 15}#

#= frac{10 - 4 sqrt 15 + 10 sqrt 5 - 4*5 sqrt 3}{100 - 16*15}#

Answer 2 · 2018-06-12T15:55:55

#(5-2sqrt15+5sqrt5-2sqrt75)/(-70)#

#(1+sqrt5)/(10+4sqrt15)#

Multiply by the conjugate which is the denominator with the sign changed over itself:

#(10-4sqrt15)/(10-4sqrt15)#

#(1+sqrt5)/(10+4sqrt15)*(10-4sqrt15)/(10-4sqrt15)#

FOIL:

#(10-4sqrt15+10sqrt5-4sqrt75)/(100-40sqrt15+40sqrt15-16*15)#

#(5-2sqrt15+5sqrt5-2sqrt75)/(-70)#