" (i) "(1)/(sqrt(2))" (ii) "7sqrt(5)

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))

Show that the following numbers are irrational.(1)/(sqrt(2)) (ii) 7sqrt(5)

Rationalise the denominators of the following : (i) (1)/(sqrt(7)) (ii) (1)/(sqrt(7)-sqrt(6)) (iii) (1)/(sqrt(5)+sqrt(2)) (iv) (1)/(sqrt(7)-2)

Rationalise the denominators of the following : (i) (1)/(sqrt(7)) (ii) (1)/(sqrt(7)-sqrt(6)) (iii) (1)/(sqrt(5)+sqrt(2)) (iv) (1)/(sqrt(7)-2)

Show that the following numbers are irrational. 1/(sqrt(2)) (ii) 7sqrt(5)

Rationalise the denominators of the following: (i) 1/(sqrt(7)) (ii) 1/(sqrt(7)-sqrt(6)) (iii) 1/(sqrt(5)+sqrt(2)) (iv) 1/(sqrt(7)-2)

Prove that the following are irrationals (1) (1)/sqrt(2) (2) 7sqrt(5) (3)6+sqrt(2)

Rationalise the denominators of the following : i) (1)/(3+sqrt(2)) ii) (1)/(sqrt(7)-sqrt(6)) iii) (1)/(sqrt(7)) iv) (sqrt(6))/(sqrt(3)-sqrt(2))

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))

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2