Two Too Many Toos

Evaluating $\sqrt[2]{\frac {2(22)(2+2)(222-22)(2222+222+22+2)} {((222)(2(22)+2(22))-(22(2(22)+2(22)))(2^{(2)(2)(2)+2}+2^{(2)(2)+2+\frac{2}{2}}+2^{(2)(2)+2}+2^{2+2}+2)}}$

$(22)(2+2)(222-22)$ is equivilient to $(222)(2(22)+2(22))-22(2(22)+2(22))$ after factoring

Canceling them out, we have

$\sqrt[2]{\frac {2(2222+222+22+2)} {(2^{(2)(2)(2)+2}+2^{(2)(2)+2+\frac{2}{2}}+2^{(2)(2)+2}+2^{2+2}+2)}}$

$=\sqrt[2]{\frac {2(2468)} {(2^{10}+2^{7}+2^{6}+2^{4}+2)}}$

$=\sqrt[2]{\frac {2(2468)} {1234}}$

$=\sqrt[2]{\frac {4(1234)} {1234}}$

$=\sqrt[2]{4}$

$=2$ just as you guessed.