(4)/((sqrt(7)+sqrt(3)))

The value of (1)/(sqrt(7-4sqrt(3))) is closest to

(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3))-(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3))

1/(sqrt(7)+sqrt(3))\times (sqrt(7)-sqrt(3))/(sqrt(7)-sqrt(3))

If (4+3sqrt(3))/(sqrt(7+4sqrt(3)))=a+sqrt(b), then (a,b) is

given x=(sqrt(7)+sqrt(3))/(sqrt(7)-sqrt(3)),y=(sqrt(7)-sqrt(3))/(sqrt(7)+sqrt(3)) find the value of x^(4)+y^(4)+(x+y)^(4)

rationalise (4)/(2+sqrt(3)+sqrt(7))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2