Question

Be in simplified radical form look at photo for equation

Answer 1

If $m_1 = 12$ and $m_2 = 30$, we have

$\dfrac{r_1}{r_2} = \dfrac{\sqrt{m_2}}{\sqrt{m_1}}=\sqrt{\dfrac{m_2}{m_1}}=\sqrt{\dfrac{30}{12}}=\sqrt{\dfrac{5}{2}}$

If we multiply both numerator and denominator by $\sqrt{2}$, we have

$\sqrt{\dfrac{5}{2}} = \dfrac{\sqrt{5}}{\sqrt{2}}= \dfrac{\sqrt{5}}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{10}}{2}$