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

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)

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

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

The direction ratios of normal of a plane passing through two points (0,1, 0) & (0, 0, 1) and makes an angle pi/4 with the plane y-z-5=0 are (A) (2,-sqrt2,sqrt2) (B) (sqrt2,-1,1) (C) (sqrt2,1,1) (D) (2,sqrt2,1)

Set of value of m for which a chord of slope m of the circle x^2+y^2=4 touches parabola y^2=4x is (A) (-oo , -sqrt((sqrt2 -1)/2)] uu [sqrt((sqrt2 -1)/2) , oo) (B) (-oo , -1) uu (1, oo ) (C) (-1,1) (D) (-oo , oo)

The matrix A=[{:(1/sqrt2,1/sqrt2),((-1)/sqrt2,(-1)/sqrt2):}] is

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

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)