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3\sqrt{\frac{6+2}{3}}
Multiply 2 and 3 to get 6.
3\sqrt{\frac{8}{3}}
Add 6 and 2 to get 8.
3\times \frac{\sqrt{8}}{\sqrt{3}}
Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.
3\times \frac{2\sqrt{2}}{\sqrt{3}}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
3\times \frac{2\sqrt{2}\sqrt{3}}{3}
The square of \sqrt{3} is 3.
3\times \frac{2\sqrt{6}}{3}
To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.
2\sqrt{6}
Cancel out 3 and 3.