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\sqrt{324+\left(\frac{144}{\sqrt{3}}\right)^{2}}
Calculate 18 to the power of 2 and get 324.
\sqrt{324+\left(\frac{144\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)^{2}}
Rationalize the denominator of \frac{144}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
\sqrt{324+\left(\frac{144\sqrt{3}}{3}\right)^{2}}
The square of \sqrt{3} is 3.
\sqrt{324+\left(48\sqrt{3}\right)^{2}}
Divide 144\sqrt{3} by 3 to get 48\sqrt{3}.
\sqrt{324+48^{2}\left(\sqrt{3}\right)^{2}}
Expand \left(48\sqrt{3}\right)^{2}.
\sqrt{324+2304\left(\sqrt{3}\right)^{2}}
Calculate 48 to the power of 2 and get 2304.
\sqrt{324+2304\times 3}
The square of \sqrt{3} is 3.
\sqrt{324+6912}
Multiply 2304 and 3 to get 6912.
\sqrt{7236}
Add 324 and 6912 to get 7236.
6\sqrt{201}
Factor 7236=6^{2}\times 201. Rewrite the square root of the product \sqrt{6^{2}\times 201} as the product of square roots \sqrt{6^{2}}\sqrt{201}. Take the square root of 6^{2}.