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\sqrt{\frac{1.6\times 4\times 8.85\times 11.9}{0.889}}
Cancel out 2 in both numerator and denominator.
\sqrt{\frac{6.4\times 8.85\times 11.9}{0.889}}
Multiply 1.6 and 4 to get 6.4.
\sqrt{\frac{56.64\times 11.9}{0.889}}
Multiply 6.4 and 8.85 to get 56.64.
\sqrt{\frac{674.016}{0.889}}
Multiply 56.64 and 11.9 to get 674.016.
\sqrt{\frac{674016}{889}}
Expand \frac{674.016}{0.889} by multiplying both numerator and the denominator by 1000.
\sqrt{\frac{96288}{127}}
Reduce the fraction \frac{674016}{889} to lowest terms by extracting and canceling out 7.
\frac{\sqrt{96288}}{\sqrt{127}}
Rewrite the square root of the division \sqrt{\frac{96288}{127}} as the division of square roots \frac{\sqrt{96288}}{\sqrt{127}}.
\frac{4\sqrt{6018}}{\sqrt{127}}
Factor 96288=4^{2}\times 6018. Rewrite the square root of the product \sqrt{4^{2}\times 6018} as the product of square roots \sqrt{4^{2}}\sqrt{6018}. Take the square root of 4^{2}.
\frac{4\sqrt{6018}\sqrt{127}}{\left(\sqrt{127}\right)^{2}}
Rationalize the denominator of \frac{4\sqrt{6018}}{\sqrt{127}} by multiplying numerator and denominator by \sqrt{127}.
\frac{4\sqrt{6018}\sqrt{127}}{127}
The square of \sqrt{127} is 127.
\frac{4\sqrt{764286}}{127}
To multiply \sqrt{6018} and \sqrt{127}, multiply the numbers under the square root.