`3sqrt(4)+2sqrt(9)+5sqrt(4)-sqrt(1)-4sqrt(9)`

Arrange the following in decending order sqrt(3) - sqrt(2), sqrt(4) - sqrt(3), sqrt(5) - sqrt(4), sqrt(2) - 1 .

4 sin 27^(0)= 1) sqrt(5+sqrt(5))+sqrt(3-sqrt(5)) 2) sqrt(5-sqrt(5))+sqrt(3+sqrt(5) 3) sqrt(5+sqrt(5))-sqrt(3-sqrt(5)) 4) sqrt(5+sqrt(5))+sqrt(3+sqrt(5)

The greatest among sqrt(7) - sqrt(5) , sqrt(5) - sqrt(3) , sqrt(9) - sqrt(7) , sqrt(11) - sqrt(9) is

(4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))

(3sqrt(2))/(sqrt(6)-sqrt(3))-(4sqrt(3))/(sqrt(6)-sqrt(2))-(6)/(sqrt(8)-sqrt(12))=? a.sqrt(3)-sqrt(2)b*sqrt(3)+sqrt(2)c.5sqrt(3)d.1

1/(1-sqrt(2))+ 1/(sqrt(2)-sqrt(3))+1/(sqrt(3)-sqrt(4))+..........+1/(sqrt(8)-sqrt(9))

Evaluate the following: (i) sqrt(-25)xx(-81) (ii) sqrt(-36)xxsqrt(16) (iii) 4sqrt(-4)+5sqrt(-9)-3sqrt(-16)

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

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