Rationalize: ` (sqrt3 - 1) / ( sqrt3 + 1 )`

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

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

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

If both a and b are rational numbers, find the values of a and b in each of the following equalities : (sqrt(3)-1)/(sqrt(3)+1)=a+bsqrt(3)

find the general solution of the equation (sqrt3-1)sintheta+(sqrt3 + 1)costheta = 2

The value of x in (0,pi/2) satisfying the equation, (sqrt3-1)/sin x+ (sqrt3+1)/cosx=4sqrt2 is -

Show that tan 75^(@) = (sqrt3) +(1 )/( sqrt3 -1) = 2 + sqrt3. Hence deduce that tan 75^(@) - cot 75^(@) = 4 sin 60^(@).

The sum of rational term(s) in (sqrt3 + 2^(1/3) + 5^(1/4))^8 is equal to

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

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