If [tex]m_1 = 12[/tex] and [tex]m_2 = 30[/tex], we have
[tex]\dfrac{r_1}{r_2} = \dfrac{\sqrt{m_2}}{\sqrt{m_1}}=\sqrt{\dfrac{m_2}{m_1}}=\sqrt{\dfrac{30}{12}}=\sqrt{\dfrac{5}{2}}[/tex]
If we multiply both numerator and denominator by [tex]\sqrt{2}[/tex], we have
[tex]\sqrt{\dfrac{5}{2}} = \dfrac{\sqrt{5}}{\sqrt{2}}= \dfrac{\sqrt{5}}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{10}}{2}[/tex]
