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(A) For equation $I$: $x^{2}-7 \sqrt{7} x+84=0$Splitting the middle term: $x^{2}-4 \sqrt{7} x-3 \sqrt{7} x+84=0$$x(x-4 \sqrt{7})-3 \sqrt{7}(x-4 \sqrt{

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if $x > y$

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(A) For equation $I$: $x^{2}-7 \sqrt{7} x+84=0$Splitting the middle term: $x^{2}-4 \sqrt{7} x-3 \sqrt{7} x+84=0$$x(x-4 \sqrt{7})-3 \sqrt{7}(x-4 \sqrt{7})=0$$(x-4 \sqrt{7})(x-3 \sqrt{7})=0$So,$x = 4 \sqrt{7}$ or $x = 3 \sqrt{7}$.Since $\sqrt{7} \approx 2.646$,$x \approx 10.58$ or $x \approx 7.94$.For equation $II$: $y^{2}-5 \sqrt{5} y+30=0$Splitting the middle term: $y^{2}-3 \sqrt{5} y-2 \sqrt{5} y+30=0$$y(y-3 \sqrt{5})-2 \sqrt{5}(y-3 \sqrt{5})=0$$(y-3 \sqrt{5})(y-2 \sqrt{5})=0$So,$y = 3 \sqrt{5}$ or $y = 2 \sqrt{5}$.Since $\sqrt{5} \approx 2.236$,$y \approx 6.71$ or $y \approx 4.47$.Comparing the values: All values of $x$ are greater than all values of $y$.Therefore,$x > y$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $x^{2}-7 \sqrt{7} x+84=0$
$II.$ $y^{2}-5 \sqrt{5} y+30=0$

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Solve the given two equations and select the correct answer from the given options.$I.$ $x^{2}-7 \sqrt{7} x+84=0$$II.$ $y^{2}-5 \sqrt{5} y+30=0$