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\frac{0}{3}\sqrt{\frac{1\times 5+3}{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Anything times zero gives zero.
0\sqrt{\frac{1\times 5+3}{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Zero divided by any non-zero number gives zero.
0\sqrt{\frac{5+3}{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Multiply 1 and 5 to get 5.
0\sqrt{\frac{8}{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Add 5 and 3 to get 8.
0\times \frac{\sqrt{8}}{\sqrt{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.
0\times \frac{2\sqrt{2}}{\sqrt{5}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{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}.
0\times \frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
0\times \frac{2\sqrt{2}\sqrt{5}}{5}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
The square of \sqrt{5} is 5.
0\times \frac{2\sqrt{10}}{5}\times \frac{2}{3}\sqrt{\frac{6\times 3+2}{3}}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
0\times \frac{2\sqrt{10}}{5}\sqrt{\frac{6\times 3+2}{3}}
Multiply 0 and \frac{2}{3} to get 0.
0\times \frac{2\sqrt{10}}{5}\sqrt{\frac{18+2}{3}}
Multiply 6 and 3 to get 18.
0\times \frac{2\sqrt{10}}{5}\sqrt{\frac{20}{3}}
Add 18 and 2 to get 20.
0\times \frac{2\sqrt{10}}{5}\times \frac{\sqrt{20}}{\sqrt{3}}
Rewrite the square root of the division \sqrt{\frac{20}{3}} as the division of square roots \frac{\sqrt{20}}{\sqrt{3}}.
0\times \frac{2\sqrt{10}}{5}\times \frac{2\sqrt{5}}{\sqrt{3}}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
0\times \frac{2\sqrt{10}}{5}\times \frac{2\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}
Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.
0\times \frac{2\sqrt{10}}{5}\times \frac{2\sqrt{5}\sqrt{3}}{3}
The square of \sqrt{3} is 3.
0\times \frac{2\sqrt{10}}{5}\times \frac{2\sqrt{15}}{3}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
0
Anything times zero gives zero.