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2+\sqrt{18}-\frac{2}{\sqrt{2}}+3\sqrt{\frac{1}{3}}
Calculate \sqrt[3]{8} and get 2.
2+3\sqrt{2}-\frac{2}{\sqrt{2}}+3\sqrt{\frac{1}{3}}
Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.
2+3\sqrt{2}-\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3\sqrt{\frac{1}{3}}
Rationalize the denominator of \frac{2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
2+3\sqrt{2}-\frac{2\sqrt{2}}{2}+3\sqrt{\frac{1}{3}}
The square of \sqrt{2} is 2.
2+3\sqrt{2}-\sqrt{2}+3\sqrt{\frac{1}{3}}
Cancel out 2 and 2.
2+3\sqrt{2}-\sqrt{2}+3\times \frac{\sqrt{1}}{\sqrt{3}}
Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.
2+3\sqrt{2}-\sqrt{2}+3\times \frac{1}{\sqrt{3}}
Calculate the square root of 1 and get 1.
2+3\sqrt{2}-\sqrt{2}+3\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
2+3\sqrt{2}-\sqrt{2}+3\times \frac{\sqrt{3}}{3}
The square of \sqrt{3} is 3.
2+3\sqrt{2}-\sqrt{2}+\sqrt{3}
Cancel out 3 and 3.
2+2\sqrt{2}+\sqrt{3}
Combine 3\sqrt{2} and -\sqrt{2} to get 2\sqrt{2}.