`(sqrt 11- sqrt 7)(sqrt 11+ sqrt 7)`

Simplify {(\sqrt 5+\sqrt 3)\times (\sqrt 5 - \sqrt 3)}/(\sqrt 7- \sqrt 3)\times (\sqrt 7+ \sqrt 3)/(\sqrt 7+\sqrt 3)

If sqrt (7 sqrt (7 sqrt7 sqrt7 sqrt7)) = 7 ^(x) then find the value of x

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).

Find the value of the following: (i) log_(10) 2 + log_(10) 5 (ii) log_(3) (sqrt(11)-sqrt2) + log_(3) (sqrt11+sqrt2) (iii) log_(7) 35 - log_(7) 5

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}

Prove that: 1/(3-sqrt(8))-1/(sqrt(8)-\ sqrt(7))+1/(sqrt(7)-\ sqrt(6))-1/(sqrt(6)-\ sqrt(5))+1/(sqrt(5)-2)=5

Simplify : (7)/(sqrt(17) - 2sqrt3)-( 3)/(sqrt(17) +2sqrt3)

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

Simplify (7sqrt3)/(sqrt10+sqrt3)-(2sqrt5)/(sqrt6+sqrt5)-(3sqrt2)/(sqrt15+3sqrt2)