`(1)/(sqrt(3))times(sqrt(2))/(sqrt(3))=`

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

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

If sqrt(3) = 1.73 find the value of : (2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)-1)/(sqrt(3)+1)-(sqrt(3)+1)/(sqrt(3)-1) .

((sqrt(5)-3))/((sqrt(5)-3))times((sqrt(5)-3))/((sqrt(5)+3))

Rationalise the denominator of each of the following (i) (sqrt(3)+\ 1)/(sqrt(2)) (ii) (sqrt(2)+\ sqrt(5))/(sqrt(3)) (iii) (3sqrt(2))/(sqrt(5))

Angles of a triangle are in 4:1:1 ration. The ratio between its greatest side and perimeter is 3/(2+sqrt(3)) (b) (sqrt(3))/(2+sqrt(3)) (sqrt(3))/(2-sqrt(3)) (d) 1/(2+sqrt(3))

(sqrt(2)+sqrt(3))times(sqrt(3)+sqrt(8))

(3+sqrt(2))(2-sqrt(3))(3-sqrt(2))(2+sqrt(3))

Simplify : (1)/(sqrt(3)+sqrt(2))-(1)/(sqrt(3)-sqrt(2))+(2)/(sqrt(2)+1)

The value of log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo) is