`(4+sqrt2)/(2+sqrt2)=a-sqrtb`

Rationalise the denominator and simplify: (i) (4sqrt(3)+5sqrt(2))/(sqrt(48)+\ sqrt(18)) (ii) (2sqrt(3)-\ sqrt(5))/(2\ sqrt(2)+\ 3sqrt(3))

If sqrt(9+sqrt48-sqrt32-sqrt24)=sqrta-sqrtb+2 ,where a,b inN , then find the value of a + b.

If a =( 4sqrt(6))/(sqrt(2)+sqrt(3)) then the value of (a+2sqrt(2))/(a-2sqrt(2))+(a+2sqrt(3))/(a-2sqrt(3))

(4(sqrt(6) + sqrt(2)))/(sqrt(6) - sqrt(2)) - (2 + sqrt(3))/(2 - sqrt(3)) =

Simplify each of the following : (i) 3/(5-sqrt(3))+2/(5+sqrt(3)) (ii) (4+sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (iii) (sqrt(5)-2)/(sqrt(5)+2)-(sqrt(5)+2)/(sqrt(5)-2)

Solve the equation: (4sqrt(cos x/2)-5-(sqrt(2))/2)^2+ sqrt(2)(4sqrt(cos x/2)-5-(sqrt(2))/2)-(cosx)/2=0

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

The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+(5sqrt2-7/6)sqrt(2)+17-12sqrt(2)/(16)+..+++..+ add.infty is

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

If alpha, betaepsilon(0, pi/2) and if sin^4alpha+4cos^4beta+2=4sqrt2 sinalphacosbeta then the value of cos(alpha+beta)-cos(alpha-beta) is (A) sqrt2 (B) 1/sqrt2 (C) -1/sqrt2 (D) -sqrt2