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\sqrt{6^{2}\left(\sqrt{2}\right)^{2}-3}
Expand \left(6\sqrt{2}\right)^{2}.
\sqrt{36\left(\sqrt{2}\right)^{2}-3}
Calculate 6 to the power of 2 and get 36.
\sqrt{36\times 2-3}
The square of \sqrt{2} is 2.
\sqrt{72-3}
Multiply 36 and 2 to get 72.
\sqrt{69}
Subtract 3 from 72 to get 69.