`|[2+sqrt 2,3-sqrt 3],[3+sqrt 3, 2-sqrt2]|`

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

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

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

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

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (a) (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (c) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

if sqrt2=1.414and sqrt3=1.732 then find the value of 4/(3sqrt3-2sqrt2)+3/(3sqrt3+2sqrt2)

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)