Evaluate:

$\sqrt{\dfrac{14.4}{22.5}}$

$\sqrt{\dfrac{14.4}{22.5}}\\[1em] = \dfrac{\sqrt{144 \times 10}}{\sqrt{225 \times 10}}\\[1em] = \dfrac{\sqrt{144}}{\sqrt{225}}\\[1em] = \dfrac{\sqrt{(2\times2)\times(2\times2)\times(3\times3)}}{\sqrt{(3\times3)\times(5\times5)}}\\[1em] = \dfrac{2\times2\times3}{3\times5}\\[1em] = \dfrac{12}{15}\\[1em] = 0.8$

$\sqrt{\dfrac{14.4}{22.5}} = 0.8$