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