`(frac{sqrt 3 - sqrt 2}{sqrt 3+ sqrt 2})^2`

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

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

Rationalize the denominator 1/(sqrt 3 - sqrt 2) - 2/(sqrt 5 - sqrt 3) + 3/(sqrt 5 - sqrt 2)

Examine whether the following numbers are rational or irrational : (2 sqrt3 - 3 sqrt2) (2sqrt3 + 3 sqrt2)

Find : (sqrt5+sqrt2)(sqrt3+sqrt2)

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

Solve: (sqrt 3+ sqrt2)(sqrt2-sqrt3)

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).

Rationales the denominator and simplify: (i) (sqrt(3)-\ sqrt(2))/(sqrt(3)\ +\ sqrt(2)) (ii) (5+2\ sqrt(3))/(7+4\ sqrt(3))