Solve `(sqrt3-sqrt2)(2-sqrt2)`

Solve (sqrt3 +sqrt2)^x + (sqrt3 -sqrt2)^x= 10 .

(sqrt5+sqrt2)(sqrt3+sqrt2)

Simplify: (sqrt5-sqrt2)(sqrt2-sqrt3)

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

Solve (sqrt(2))/(sqrt(2)+sqrt(3)-sqrt(5))

Solve sqrt(2)sqrt(3)sqrt(5)

If x= (sqrt3 - sqrt2)/(sqrt3+sqrt2) and y = (sqrt3+sqrt2)/(sqrt3-sqrt2) then x^2 +xy +y^2 is a multiple of

(2sqrt3 + sqrt2)(2sqrt3-sqrt2)

Rationalise the denominator of the following (i) 2/(3sqrt3) , (ii) sqrt40/sqrt3 ,(iii) (3+sqrt2)/(4sqrt2) (iv) 16/(sqrt41-5) ,(v) (2+sqrt3)/(2-sqrt3) , (vi) sqrt6/(sqrt2+sqrt3) (vii) (sqrt3+sqrt2)/(sqrt3-sqrt2) ,(viii) (3sqrt5+sqrt3)/(sqrt5-sqrt3) , (ix) (4sqrt3+5sqrt2)/(sqrt48+sqrt18)

3/(sqrt3-sqrt2)=asqrt3-bsqrt2