Simplify: `1/(sqrt5 + sqrt4) + 1/(sqrt4 + sqrt3) + 1/(sqrt3 + sqrt2) + 1/(sqrt2 + sqrt1)`

1/(sqrt3 + sqrt2) + 1/(sqrt3 -sqrt2)=

sqrt 2(sqrt 2+1) - sqrt 2 (1+sqrt2) =?

Simplify: 2/(sqrt(5)+\ sqrt(3))+1/(sqrt(3)+\ sqrt(2))-3/(sqrt(5)+\ sqrt(2))

Prove that cot 7 ""(1^(@))/(2) = sqrt2 + sqrt3 + sqrt4 + sqrt6 = (sqrt3 + sqrt2) (sqrt2 +1 ).

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

Find (sqrt3 - sqrt 2)/(sqrt 3+sqrt 2) -(sqrt3 + sqrt 2)/(sqrt 3-sqrt 2) +1/(sqrt2+1)-1/(sqrt2-1)

The sum of (1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/( 4 sqrt3 + 3 sqrt4 ) +...+(1)/( 25 sqrt 24 + 24 sqrt25) is

Simplify: (1)/(sqrt(3+2sqrt(2)))+(1)/(sqrt(3+2sqrt(2)))

Rationalize the denominator: (2 + sqrt 3)/(2 - sqrt 3) + (2 - sqrt 3)/(2 + sqrt 3) + (sqrt 3 - 1)/(sqrt 3 + 1)

Rationalise the denominator and simplify: (i) (4sqrt(3)+5sqrt(2))/(sqrt(48)+\ sqrt(18)) (ii) (2sqrt(3)-\ sqrt(5))/(2\ sqrt(2)+\ 3sqrt(3))