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

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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:

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

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

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