`(sqrt 3 + sqrt 2 ) (sqrt 3 - sqrt 2)`

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

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

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

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

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

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

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

Express the following in the form a+bi, where a and b are real numbers ((3 + sqrt5i) (3-sqrt5i))/((sqrt3+sqrt2i)- (sqrt3-sqrt2i))

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

The value of sqrt(3-2\ sqrt(2)) is (a) sqrt(2)-1 (b) sqrt(2)+1 (c) sqrt(3)-sqrt(2) (d) sqrt(3)+\ sqrt(2)