" (iii) "(4)/(2+sqrt(3)+sqrt(7))

rationalise (4)/(2+sqrt(3)+sqrt(7))

Show that (i)" "{((3+2i))/((2-3i))+((3-2i))/((2+3i))} is purely real, (ii)" "{((sqrt(7)+i sqrt(3)))/((sqrt(7)-i sqrt(3)))+((sqrt(7)- i sqrt(3)))/((sqrt(7) + i sqrt(3)))} is purely real.

if (4)/(2+sqrt(3)+sqrt(7))=sqrt(a)+sqrt(b)-sqrt(c) then :

Simplify the following expressions: (i)\ (4+\ sqrt(7))\ (3+sqrt(2)) (ii)\ (3+sqrt(3))\ (5-sqrt(2)) (iii)\ (sqrt(5)-2)\ (sqrt(3)-sqrt(5))

(i) 3sqrt(5) by 2sqrt(5) ,(ii) 6sqrt(15) by 4sqrt(3) , (iii) 2sqrt(6) by 3sqrt(3) (iv) 3sqrt(8) by 3sqrt(2) ,(v) sqrt(10) by sqrt(40) , (vi) 3sqrt(28) by 2sqrt(7)

Rationales the denominator and simplify: (sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))( ii) (5+2sqrt(3))/(7+4sqrt(3))

sqrt(2)+sqrt(3)+sqrt(7)-(1)/(sqrt(2)+sqrt(3)+sqrt(7))=?

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 the following expressions: (4+sqrt(7))(3+sqrt(2))( (ii) (3+sqrt(3))(5-sqrt(2))(sqrt(5)-2)(sqrt(3)-sqrt(5))

In each of the following determine rational number a and b:(3+sqrt(2))/(3-sqrt(2))=a+b sqrt(2) (ii) (5+3sqrt(3))/(7+4sqrt(3))=a+b sqrt(3)