If x = 10³ × 0.0099, y = 10^-2 × 110, find the value of $\sqrt{\dfrac{x}{y}}$.

Substituting value of x and y in $\sqrt{\dfrac{x}{y}}$ we get,

$\Rightarrow \sqrt{\dfrac{x}{y}} = \sqrt{\dfrac{10^3 \times 0.0099}{10^{-2} \times 110}} \\[1em] = \sqrt{\dfrac{9.9}{10^{-2} \times 110}} \\[1em] = \sqrt{\dfrac{9.9 \times 10^2}{110}} \\[1em] = \sqrt{\dfrac{990}{110}} \\[1em] = \sqrt{9} = 3.$

Hence, $\sqrt{\dfrac{x}{y}} = 3.$