(i) `sqrt(12+6sqrt3)-sqrt3` is (ii)`sqrt((6-sqrt5)+sqrt(14+6sqrt5))` (iii) `sqrt(3+2sqrt2)-2sqrt2`

(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))

(sqrt(6)+sqrt(5)+ 1/(sqrt(6)+sqrt(5)))^2

Choose the incorrect relation(s) from the following : (I ) sqrt(6) + sqrt(2) = sqrt(5) + sqrt(3) (ii) sqrt(6) + sqrt( 2) lt sqrt(5) + sqrt (3) (iii) sqrt(6) + sqrt(2) gt sqrt(5) + sqrt(3)

find the values of a and b in each of the following (i) (5+2sqrt3)/(7+4sqrt3) = a-6sqrt3 (ii) (3-sqrt5)/(3+2sqrt5)= asqrt5-(19/11) (iii) (sqrt2+sqrt3)/(3sqrt2-2sqrt3)=2-bsqrt6 (iv) (7+sqrt5)/(7-sqrt5)-(7-sqrt5)/(7+sqrt5)=a+(7/11)bsqrt5

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))

Rationalise the denominator of the following (i) 2/(3sqrt3) , (ii) sqrt40/sqrt3 ,(iii) (3+sqrt2)/(4sqrt2) (iv) 16/(sqrt41-5) ,(v) (2+sqrt3)/(2-sqrt3) , (vi) sqrt6/(sqrt2+sqrt3) (vii) (sqrt3+sqrt2)/(sqrt3-sqrt2) ,(viii) (3sqrt5+sqrt3)/(sqrt5-sqrt3) , (ix) (4sqrt3+5sqrt2)/(sqrt48+sqrt18)

(sqrt(6)+sqrt(3))/(sqrt(5)+sqrt(2))

Simplify: (i) (3sqrt(2)-2sqrt(2))/(3sqrt(2)+\ 2sqrt(3))+(sqrt(12))/(sqrt(3)-\ sqrt(2)) (ii) (sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3))+(sqrt(5)-\ sqrt(3))/(sqrt(5)+\ sqrt(3))