de-Broglie's wavelength is given by the equation $\lambda=\frac{h}{p}$
To find the ratio of the wavelength, we need the ratio of $p$, where $p=m v$
$$
p=m v=\sqrt{m^2 v^2}=\sqrt{2 m\left(\frac{1}{2} m v^2\right)}=\sqrt{2 m K}
$$
where, $m$ is mass and $K$ is kinetic energy.
Hence, the ratio of the wavelength is
$$
\begin{aligned}
\frac{\lambda_1}{\lambda_2} & =\frac{\left(h / p_1\right)}{\left(h / p_2\right)}=\frac{p_2}{p_1} \\
& =\sqrt{\frac{2 m_2 K_2}{2 m_1 K_1}}=\sqrt{\left(\frac{m_2}{m_1}\right)\left(\frac{K_2}{K_1}\right)} \\
& =\sqrt{3\left(\frac{1}{2}\right)}=\sqrt{\frac{3}{2}}=\sqrt{3}: \sqrt{2}
\end{aligned}
$$