Prove that `(sqrt(7)-sqrt(3))ltsqrt(5)-1`

(2sqrt(7))/(sqrt(5)-sqrt(3))

7/(sqrt5-sqrt3) =

show that (sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))times(sqrt(7)-sqrt(5))/(sqrt(7)-sqrt(5)) =frac{(sqrt(7)-sqrt(5))^(2)}{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

(1)/(sqrt(2)+sqrt(5)-sqrt(7))

Prove that log_(7) log_(7)sqrt(7sqrt((7sqrt7))) = 1-3 log_(7) 2 .

Prove that 5sqrt(7) is irrational.

(sqrt(5)+sqrt(3))(sqrt(7)-sqrt(3))

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

(7+3sqrt5)/(7-3sqrt5)=