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\frac{2}{11}\times 6\sqrt{3}\times \frac{5}{8}\sqrt{147}
Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.
\frac{2\times 6}{11}\sqrt{3}\times \frac{5}{8}\sqrt{147}
Express \frac{2}{11}\times 6 as a single fraction.
\frac{12}{11}\sqrt{3}\times \frac{5}{8}\sqrt{147}
Multiply 2 and 6 to get 12.
\frac{12\times 5}{11\times 8}\sqrt{3}\sqrt{147}
Multiply \frac{12}{11} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{60}{88}\sqrt{3}\sqrt{147}
Do the multiplications in the fraction \frac{12\times 5}{11\times 8}.
\frac{15}{22}\sqrt{3}\sqrt{147}
Reduce the fraction \frac{60}{88} to lowest terms by extracting and canceling out 4.
\frac{15}{22}\sqrt{3}\times 7\sqrt{3}
Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.
\frac{15\times 7}{22}\sqrt{3}\sqrt{3}
Express \frac{15}{22}\times 7 as a single fraction.
\frac{105}{22}\sqrt{3}\sqrt{3}
Multiply 15 and 7 to get 105.
\frac{105}{22}\times 3
Multiply \sqrt{3} and \sqrt{3} to get 3.
\frac{105\times 3}{22}
Express \frac{105}{22}\times 3 as a single fraction.
\frac{315}{22}
Multiply 105 and 3 to get 315.