`frac{6 sqrt 7 + sqrt 2}{sqrt 7 - sqrt 2}`

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

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

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).

frac{1}{sqrt7-4} frac{1}{sqrt11-7}

solve the equations: frac{2}{sqrt x} + frac{3}{sqrt y} =2 and frac{4}{sqrt x} - frac{9}{sqrt y} =-1

(4(sqrt(6) + sqrt(2)))/(sqrt(6) - sqrt(2)) - (2 + sqrt(3))/(2 - sqrt(3)) =

(sqrt(7)+2sqrt(3))(sqrt(7)-2sqrt(3))

Write in ascending order: 6 sqrt(5) , 7 sqrt(3) and 8 sqrt(2)

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