Solve $\sqrt{\frac{2\times (9\times {10}^9)(1.6\times {10}^{-19})\left(47\right)(1.6\times {10}^{-19})}{(1.67\times {10}^{-27})(2.5\times {10}^{-14})}}$

$=\sqrt{\frac{2\times 9\times {10}^9\times 1.6\times {10}^{-19}\times 47\times 1.6\times {10}^{-19}}{1.67\times {10}^{-27}\times 2.5\times {10}^{-14}}}$
$=\sqrt{\frac{2\times 9\times (1.6{)}^2\times 47}{\left(1.67\right)\times \left(2.5\right)}\times {10}^9+19-19+27+14}$
$=1.6\times 1.3\sqrt{\frac{2\times 47\times {10}^{12}}{1.67\times 2.5}}$
$=1.6\times 3\times {10}^2\sqrt{\frac{2\times 47}{1.67\times 2.5}}$
$=48\times {10}^5\sqrt{22.52}$
$=48\times {10}^5\times 4.75$
$=227.79\times {10}^5$