Question

Simplify this please:

\(\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2} \)

Answer 1

sqrt(sqrt(5) +2) = sqrt(5-4) / sqrt(sqrt(5) -2) = 1/ sqrt(sqrt(5) -2)
added to sqrt(sqrt(5) -2)
we have
(1 + sqrt(5) -2) / sqrt(sqrt(5) -2)
= (sqrt(5) -1) / sqrt(sqrt(5) -2)
also sqrt(sqrt(5) -2) = sqrt(5-4) / sqrt(sqrt(5) +2)

substituting,
sqrt(sqrt(5) +2) (sqrt(5) -1)

lol..maybe not simplified much..hmm

Answer 2

ohh wait,,leme try another way,,
let sqrt(sqrt(5) -2) = b
and
sqrt(sqrt(5) +2) = a
we need to find a+b
we know (a+b)^2 = a^2 + b^2 + 2ab
substituting,
(a+b)^2 = sqrt(5) +2 + sqrt(5) -2 + 2 (sqrt ( 5-4))
=>a+b = sqrt( 2sqrt(5) +2)

maybe this helps

Answer 3

ah nice work .. thank you ..