The value of the fifth root of $10^{10^{10}}$ is
$10^{2 \times 10^9}$
$10^{20 \times 10^9}$
$10^{10^2}$
$10^{2^{10}}$
The value of $\sqrt {[12\sqrt 5 + 2\sqrt {(55)} ]} $ is
${a^{m{{\log }_a}n}} = $
If $x = {{\sqrt 5 + \sqrt 2 } \over {\sqrt 5 - \sqrt 2 }},y = {{\sqrt 5 - \sqrt 2 } \over {\sqrt 5 + \sqrt 2 }},$ then $3{x^2} + 4xy - 3{y^2} = $
If ${a^x} = {(x + y + z)^y},{a^y} = {(x + y + z)^z}$, ${a^z} = {(x + y + z)^x},$ then
If $x = 3 - \sqrt {5,} $ then ${{\sqrt x } \over {\sqrt 2 + \sqrt {(3x - 2)} }} = $