Sqrt(6-2sqrt(5))-sqrt(9+4 sqrt(5))

Question

Sqrt(6-2sqrt(5))-sqrt(9+4 sqrt(5))

Comments

V(V5-1)^2-V(V5+2)^2=V5-1-V5-2=-3

Answer 1

√(6 - 2√5)  - √(9 + 4√5) = √(5 - 2√5 + 1)  - √(5 + 4√5 + 4) =
= √[(√5)² - 2√5 + 1²]   -  √[(√5)² + 4√5 + 2²] = √(√5 - 1)²  - √(√5) + 2)²  =
= √5 - 1 - √5 - 2 = - 3