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\sqrt{\frac{9.075\times 974}{0.2\times 49\times 293\times 10^{2}}}
Cancel out 10\times 10 in both numerator and denominator.
\sqrt{\frac{8839.05}{0.2\times 49\times 293\times 10^{2}}}
Multiply 9.075 and 974 to get 8839.05.
\sqrt{\frac{8839.05}{9.8\times 293\times 10^{2}}}
Multiply 0.2 and 49 to get 9.8.
\sqrt{\frac{8839.05}{2871.4\times 10^{2}}}
Multiply 9.8 and 293 to get 2871.4.
\sqrt{\frac{8839.05}{2871.4\times 100}}
Calculate 10 to the power of 2 and get 100.
\sqrt{\frac{8839.05}{287140}}
Multiply 2871.4 and 100 to get 287140.
\sqrt{\frac{883905}{28714000}}
Expand \frac{8839.05}{287140} by multiplying both numerator and the denominator by 100.
\sqrt{\frac{176781}{5742800}}
Reduce the fraction \frac{883905}{28714000} to lowest terms by extracting and canceling out 5.
\frac{\sqrt{176781}}{\sqrt{5742800}}
Rewrite the square root of the division \sqrt{\frac{176781}{5742800}} as the division of square roots \frac{\sqrt{176781}}{\sqrt{5742800}}.
\frac{11\sqrt{1461}}{\sqrt{5742800}}
Factor 176781=11^{2}\times 1461. Rewrite the square root of the product \sqrt{11^{2}\times 1461} as the product of square roots \sqrt{11^{2}}\sqrt{1461}. Take the square root of 11^{2}.
\frac{11\sqrt{1461}}{140\sqrt{293}}
Factor 5742800=140^{2}\times 293. Rewrite the square root of the product \sqrt{140^{2}\times 293} as the product of square roots \sqrt{140^{2}}\sqrt{293}. Take the square root of 140^{2}.
\frac{11\sqrt{1461}\sqrt{293}}{140\left(\sqrt{293}\right)^{2}}
Rationalize the denominator of \frac{11\sqrt{1461}}{140\sqrt{293}} by multiplying numerator and denominator by \sqrt{293}.
\frac{11\sqrt{1461}\sqrt{293}}{140\times 293}
The square of \sqrt{293} is 293.
\frac{11\sqrt{428073}}{140\times 293}
To multiply \sqrt{1461} and \sqrt{293}, multiply the numbers under the square root.
\frac{11\sqrt{428073}}{41020}
Multiply 140 and 293 to get 41020.