(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)`

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))

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))

Simplify (i) (4+ sqrt(5))/(4-sqrt(5))+(4-sqrt(5))/(4+sqrt(5)) (ii) (1)/(sqrt(3) + sqrt(2)) - (2)/(sqrt(5)-sqrt(3)) -(2)/(sqrt(2) - sqrt(5)) (iii) (2+sqrt(3))/(2-sqrt(3)) + (2-sqrt(3))/(2+sqrt(3)) + (sqrt(3)-1)/(sqrt(3)+1) (iv) (2+sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3)) -(8sqrt(3))/(sqrt(6)+sqrt(2))

Add (i) (2sqrt(3)-5sqrt(2)) and (sqrt(3) + 2sqrt(2)) (ii) (2sqrt(2) + 5sqrt(3) - 7 sqrt(5) and (3sqrt(3)-sqrt(2) + sqrt(5)) (iii) ((2)/(3) sqrt(7) -(1)/(2)sqrt(2)+6sqrt(11)) and ((1)/(3)sqrt(7) + (3)/(2)-sqrt(11))

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)

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))

Do as directed: (i) Add : sqrt(125 + 2 sqrt(27) and - 5 sqrt(5) - sqrt(3) (ii) Add: sqrt(7) - sqrt(11) and sqrt(5) - sqrt(11) + sqrt(13) (iii) Multiply : 2 sqrt(2) by 5 sqrt(2) (iv) Multiply : (-3 + sqrt(5)) by 3 (v) Divide : 7 sqrt(5) by - 14 sqrt(125) Divide : 7 sqrt(5) by -14 sqrt(125) (vi) Divide : 2 sqrt(216) - 3 sqrt(27) by 3

The value of 5sqrt(3) + 7sqrt(2) - sqrt(6) - 23/(sqrt(2) + sqrt(3) + sqrt(6)) is: