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\frac{7\sqrt{777}}{8\left(\sqrt{777}\right)^{2}}
Rationalize the denominator of \frac{7}{8\sqrt{777}} by multiplying numerator and denominator by \sqrt{777}.
\frac{7\sqrt{777}}{8\times 777}
The square of \sqrt{777} is 777.
\frac{\sqrt{777}}{8\times 111}
Cancel out 7 in both numerator and denominator.
\frac{\sqrt{777}}{888}
Multiply 8 and 111 to get 888.