Evaluate:

$\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times (5) - (27)^\dfrac{2}{3}$

$\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times 5 - (27)^\dfrac{2}{3}\\[1em] = \dfrac{1}{2} + \Big(\dfrac{1}{0.01}\Big)^{\dfrac{1}{2}} \times 5 - (3^3)^\dfrac{2}{3}\\[1em] = \dfrac{1}{2} + \Big(\dfrac{100}{1}\Big)^{\dfrac{1}{2}} \times 5 - (3)^\dfrac{2 \times 3}{3}\\[1em] = \dfrac{1}{2} + \sqrt{100} \times 5 - (3)^2\\[1em] = \dfrac{1}{2} + 10 \times 5 - 9\\[1em] = \dfrac{1}{2} + 50 - 9\\[1em] = \dfrac{1}{2} + 41\\[1em] = \dfrac{1 + 82}{2}\\[1em] = \dfrac{83}{2}\\[1em] = 41\dfrac{1}{2}$

Hence, $\sqrt\dfrac{1}{4} + (0.01)^{-\dfrac{1}{2}} \times (5) - (27)^\dfrac{2}{3} = 41\dfrac{1}{2}$.