`(15-2sqrt(56)6)*(sqrt(7)-2sqrt(2)3)`

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

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

(root(6)(15-2sqrt(56)))*(root(3)(sqrt(7)+2sqrt(2))) =_______.

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))

Simplify by raationalising the denominator. (i) (7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)) (ii) (2sqrt(6) -sqrt(5))/(3sqrt(5)-2sqrt(6))

The value of log_(2)(sqrt(17+2sqrt(6))-sqrt(7-2sqrt(6))) is equal to

Simplify sqrt(5+2sqrt(6))+sqrt(8-2sqrt(15))

Simplify: (7sqrt(3))/(sqrt(10)+sqrt(3))-(2sqrt(5))/(sqrt(6)+sqrt(5))-(3sqrt(2))/(sqrt(15)+3sqrt(2))

sqrt(7+2sqrt(6))+sqrt(7-2sqrt(6)) =______.