(iii) `(sqrt(2)+sqrt(3))^(2)`

Simplify: (i) (2 sqrt(2) + 3 sqrt(3)) (2 sqrt(2) - 3 sqrt(3)) (ii) (2 sqrt(8) - 3 sqrt(2))^(2) (iii) (sqrt(7) + sqrt(6))^(2) (iv) (6 - sqrt(2))(2 + sqrt(3))

Show that (1)/(sqrt(2)+sqrt(3))-(2)/(sqrt(5)-sqrt(3))+(3)/(sqrt(5)-sqrt(2))=0 .

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

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

( (sqrt(2)+i sqrt(3))+(sqrt(2)-i sqrt(3)) )/( (sqrt(3)+i sqrt(2))+(sqrt(3)-i sqrt(2)) )

((2+sqrt(3))/(sqrt(2)+sqrt(2+sqrt(3)))+(2-sqrt(3))/(sqrt(2)+sqrt(2-sqrt(3))))^(2)=

simplify (sqrt(2)-sqrt(3))/2-(sqrt(2)+sqrt(3))/2

If a and b are rational numbers and (sqrt(2)+2sqrt(3))/(2sqrt(2)+sqrt(3))=a+b sqrt(6)

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

The value of ((sqrt(sqrt(3)+1)+sqrt(sqrt(3)-1))^(2)(sqrt(3)-sqrt(2)))/((sqrt(sqrt(3)+1))^(2)-(sqrt(sqrt(3)-1))^(2)) is