[7.],[" (i) "(2-sqrt(2))(2+sqrt(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))

Rationalise the denominator of each of the following. (i) (1)/(sqrt(7)) (ii) (sqrt(5))/(2sqrt(3)) (iii) (1)/(2+ sqrt(3)) (1)/(sqrt(3)) (v) (1)/((5+3sqrt(2)) (vi) (1)/(sqrt(7) - sqrt(6)) (vi) (1)/(sqrt(7) - sqrt(6)) (viii) (1+ sqrt(2))/(2-sqrt(2)) (ix) (3-2sqrt(2))/(3+2sqrt(2))

(7+sqrt2)(7-sqrt2) =

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

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

Express the result in the form x+iy, where x,y are real number i=sqrt(-1) : (i) (-5+3i)(8-7i) (ii) (-sqrt(3)+sqrt(-2))(2sqrt(3)-i) (iii) (sqrt(2)-sqrt(3)i)^(2)

State, whether the following numbers are rational or not : (i) (2+sqrt(2))^(2)" (ii) "(5+sqrt(5))(5-sqrt(5)) (iii) (sqrt(7)/(5sqrt(2)))^(2)

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

sqrt(i)-sqrt(-i)=sqrt(2)