`(3+2 sqrt(2))^(-3) + (3-2 sqrt(2))^(-3)` is (i) `189` (ii)`180` (iii)`108` (iv)`198`

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))

Simplify (i) (3-sqrt(11))(3+sqrt(11)) (ii) (-3+ sqrt(5))(-3-sqrt(3)-sqrt(5)) (iii) (3- sqrt(3))^(2) (iv) (sqrt(5) - sqrt(3))^(2) (v) (5+ sqrt(7))(2+ sqrt(5)) (vi) (sqrt(5) - sqrt(2))(sqrt(2) - sqrt(3))

z = 5+(3sqrt (2)) i then zbar (z) = (i) 43 (ii) 45 (iii) 34 (iv) 54

(sqrt(3)+i sqrt(2))(sqrt(2)+i sqrt(3))= ..........

sqrt(3i)+sqrt(-3i)=(i)+-2sqrt(3)(ii)+-sqrt(6)(iii)3(iv)3i

the value of |((3-i sqrt(2))^(2))/(1+i2)| is equal to (i) (11)/(sqrt(5)) (ii) (18)/(sqrt(7)) (iii) (5)/(sqrt(11)) (iv) (13)/(sqrt(3))

Let x=root(3)(2+sqrt5)+root(3)(2-sqrt5), then x^3+3x is equal to (i)1 (ii)2 (iii)3 (iv)4

If (5+2sqrt(6))^(x^(2)-3)+(5-2sqrt(6))^(x^(2)-3)=10 then x=(i)+-2,+-sqrt(2)(ii+-1,+-sqrt(2) (iii) +-4,+-sqrt(2)(iv)+-sqrt(5),+-sqrt(2)

If i=sqrt(-)1, then 4+5(-(1)/(2)+(i sqrt(3))/(2))^(334)+3(-(1)/(2)+(i sqrt(3))/(2))^(365) is equal to (1)1-i sqrt(3)(2)-1+i sqrt(3)(3)i sqrt(3)(4)-i sqrt(3)

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