`((sqrt(2))/(sqrt(3)))^(5)((6)/(7))^(2)`

(2sqrt(7))/(sqrt(5)-sqrt(3))

The value of (2sqrt(10))/(sqrt(5)+sqrt(2)-sqrt(7))-sqrt((sqrt(5)-2)/(sqrt(5)+2))-3/(sqrt(7)-2) is

(sqrt(3)-sqrt(5))(sqrt(3)+sqrt(5))/(sqrt(7)-2sqrt(5))

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2)) (ii) (5+2sqrt(3))/(7+4sqrt(3)) (iii) (1+sqrt(2))/(3-2sqrt(2)) (2sqrt(6)-sqrt(5))/(3sqrt(5)-2sqrt(6)) (v) (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18)) (vi) (2sqrt(3)-sqrt(5))/(2sqrt(3)+3sqrt(3))

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

(2)/(sqrt(5)+sqrt(3))-(3)/(sqrt(6)+sqrt(3))+(1)/(sqrt(6)+sqrt(5))=?

Simplify the following expressions: (3+sqrt(3))(2+sqrt(2))( ii) (5+sqrt(7))(2+sqrt(5))

Simplify the following expressions: (3+sqrt(3))(2+sqrt(2))( ii) (5+sqrt(7))(2+sqrt(5))

Simplify: (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))/(3-sqrt(5)) (ii) (1)/(2+sqrt(3))+(2)/(sqrt(5)-sqrt(3))+(1)/(2-sqrt(5))