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\frac{144\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{144}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\frac{144\sqrt{3}}{6\times 3}
The square of \sqrt{3} is 3.
8\sqrt{3}
Cancel out 3\times 6 in both numerator and denominator.