Evaluate:

$\sqrt{\dfrac{0.225}{28.9}}$

$\sqrt{\dfrac{0.225}{28.9}}\\[1em] = \sqrt{\dfrac{0.225 \times 10000}{28.9 \times 10000}}\\[1em] = \dfrac{\sqrt{225 \times 10}}{\sqrt{289 \times 1000}}\\[1em] = \dfrac{\sqrt{225}}{\sqrt{28900}}\\[1em] = \dfrac{\sqrt{(3\times3)\times(5\times5)}}{\sqrt{(2\times2)\times(5\times5)\times(17\times17)}}\\[1em] = \dfrac{3\times5}{2\times5\times17}\\[1em] = \dfrac{15}{170}\\[1em] = \dfrac{3}{34}$

$\sqrt{\dfrac{0.225}{28.9}} = \dfrac{3}{34}$