1. Find `(sqrt6-1)(-sqrt6-1)`

Find the following as a single complex number x+ iy (sqrt(6)+i5)(sqrt(6)-i(1)/(5))

(2) Find a and b if (5-sqrt6)/(5+sqrt6) =a+bsqrt 6

Evaluate the following: (sqrt(x+1)+sqrt(x-1))^6+(sqrt(x+1)-sqrt(x-1))^6

Evaluate the following: \ (sqrt(2)+1)^6+(sqrt(2)-1)^6

Find the value of (sqrt(2)+1)^6-(sqrt(2)-1)^6dot

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2) then-

Length of E F is equal to- a. 1+sqrt(3)-sqrt(6) b. \ 1+sqrt(3)-sqrt(2) c. \ sqrt(6)-1-sqrt(3) d. sqrt(2)-1+sqrt(3)

Prove that tan 7 (1^(@))/(2) = sqrt2 - sqrt3 -sqrt4 + sqrt6 = (sqrt3 - sqrt2) (sqrt2 -1).

The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+....sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))