Simiplify `(1)/(7+4sqrt3)+(1)/(2+sqrt5)`

Simplify (1)/(7+4sqrt(3))+(1)/(2+sqrt(5))

Find rationalising factors of the denominators of (i) (1)/(2sqrt(3)) (ii) (3)/(sqrt(5)) (iii) (1)/(sqrt(8))

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))

Find the conine of the angle between the lines whose direction cosines are ((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)))and((1)/(sqrt(2)),(1)/(sqrt(2)),0) .

tan^(-1)(2)=sin^(-1)(2/(sqrt(5)))=cos^(-1)(1/(sqrt(5)))

Compute the magnitude of the following vectors : veca=hati+hatj+k,vecb=2hati-7hatj-3hatk,vecc=(1)/(sqrt(3))hati+(1)/(sqrt(3))hatj-(1)/(sqrt(3))hatk

Simplify each of the following by rationalising the denominator : i) (6-4sqrt(2))/(6+4sqrt(2)) ii) (sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5)) iii) (1)/(3sqrt(2)-2sqrt(3))

Show that int_(0)^(pi//2) (dx)/(3+4 six) = (1)/(sqrt(7)) log((4+sqrt(7))/(3))

Simplify the following (sqrt(3)+1)^(5) -(sqrt(3) -1)^(5)