(iii) `1/(sqrt5+sqrt2)`

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)

Evaluate using binomial theorem: (i) (sqrt(2)+1)^(6) +(sqrt(2)-1)^(6) (ii) (sqrt(5)+sqrt(2))^(4)-(sqrt(5)-sqrt(2))^(4)

Rationalize the denominator of : (i) (2sqrt(3))/sqrt(5)" (ii) "1/(sqrt(3)-sqrt(2))

Rationalise the denominator of each the of the following : (i)(1)/(3+sqrt(5))" "(ii)(1)/(sqrt(5)-sqrt(3))" "(iii)(16)/(sqrt(41)+5)" "(iv)(30)/(5sqrt(3)+3sqrt(5))" "(v)(3-2sqrt(2))/(3+2sqrt(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))

Ratonalise the denominator in each of the following and hence evalute by taking sqrt2=1.414, sqrt3=1.732 and sqrt(5)= 2.236 upto three places of decimal. (i)4/sqrt3 , (ii) 6/sqrt6 , (iii)(sqrt10-sqrt5)/2 (iv)sqrt2/(2+sqrt2) ,(v) 1/(sqrt3+sqrt2)

4.Find the value of "1/(sqrt5+sqrt2)

Let vecb=-veci+4vecj+6veck, vecc=2veci-7vecj-10veck. If veca be a unit vector and the scalar triple product [veca vecb vecc] has the greatest value then veca is A. (1)/(sqrt(3))(hati+hatj+hatk) B. (1)/(sqrt(5))(sqrt(2)hati-hatj-sqrt(2)hatk) C. (1)/(3)(2hati+2hatj-hatk) D. (1)/(sqrt(59))(3hati-7hatj-hatk)

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))