Prove that `sqrt(5+2sqrt(6))-sqrt(5-2sqrt(6))=2sqrt(2)`

(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))

Simplify sqrt(5+2sqrt(6))+sqrt(8-2sqrt(15))

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Prove that: 1/(1+sqrt(2))+1/(sqrt(2)+sqrt(3))+1/(sqrt(3)+\ sqrt(4))+1/(sqrt(4)+sqrt(5))+1/(sqrt(5)+sqrt(6))+1/(sqrt(6)+sqrt(7))+\ 1/(sqrt(7)+sqrt(8))+1/(sqrt(8)+sqrt(9))=2

The value of sqrt(5+2sqrt(6)) is (a) sqrt(3)-sqrt(2) (b) sqrt(3)+sqrt(2) (c) sqrt(5)+sqrt(6) (d) none of these

Prove that sqrt(2)+sqrt(5) is irrational.

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x+y=2sqrt(2), then one of them will have its coordinates. (a) (sqrt(2)+sqrt(6),sqrt(2)-sqrt(6)) (b) (sqrt(2)+sqrt(3),sqrt(2)-sqrt(3)) (c) (sqrt(2)+sqrt(5),sqrt(2)-sqrt(5)) (d) none of these

Prove that: "cot"pi/(24)=sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))

2sqrt5 - sqrt5 = sqrt5