(3+sqrt(3))(2+sqrt(2))^(2)

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

Simplify the following expressions : (i) (3+sqrt(3))(2+sqrt(2)) (ii) (2+sqrt(3))(2-sqrt(3)) (iii) (sqrt(5)+sqrt(2))^(2) (iv) (sqrt(5)-sqrt(2))(sqrt(5)+sqrt(2))

After rationalising the denominator of (3 sqrt(2))/(3 sqrt(2) - 2 sqrt(2)) , we get the denominator as

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

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

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

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

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