`(3+sqrt2)(4+sqrt7)`

Simplify the following (3+sqrt(2))(4+sqrt(7))

Simplify each of the following : (i) root(5)(16) times root(5)(2)" (ii) "root(4)(243)/root(4)(3) (iii) (3+sqrt(2))(4+sqrt(7))" (iv) "(sqrt(3)-sqrt(2))^(2)

(3-sqrt7)(3+sqrt7)=?

If (3 + sqrt7)/(3 - sqrt7) = a + bsqrt7 , then ( a , b ) =

Compute the following 56+(log)_(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)_(1//2)1/(10+2sqrt(21))

Evaluate : lim_(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2)(3sqrt(2)+4sqrt(n))^(2))+(sqrt(n))/(sqrt(3)(3sqrt(3)+4sqrt(n))^(2))+.......+(1)/(49n)]

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

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

Prove that, cot 7 1/2 ^@ or tan 82 1/2 ^@ = (sqrt(3)+sqrt(2))(sqrt(2)+1) or sqrt(2)+sqrt(3)+sqrt(4)+sqrt(6)

Rationales the denominator and simplify: (i) (sqrt(3)-\ sqrt(2))/(sqrt(3)\ +\ sqrt(2)) (ii) (5+2\ sqrt(3))/(7+4\ sqrt(3))