1. Energy released in fission

If the original nucleus has mass $M$ and the total mass defect is $\Delta M$, then the energy released is

$Q = \Delta M c^2$

2. Formation of three identical daughter nuclei

Three similar daughter nuclei are formed, so the total released energy is shared among the three nuclei.

Assuming the parent nucleus was initially at rest and all three daughter nuclei get equal kinetic energy,

$3K = \Delta M c^2$

So kinetic energy of each daughter nucleus is

$K = \frac{\Delta M c^2}{3}$

3. Mass of each daughter nucleus

Since the parent nucleus of mass $M$ splits into three similar fragments, each daughter nucleus has mass approximately

$m = \frac{M}{3}$

4. Use non-relativistic kinetic energy formula

For each daughter nucleus,

$K = \frac{1}{2}mv^2$

Substitute $m = \frac{M}{3}$ and $K = \frac{\Delta M c^2}{3}$:

$\frac{1}{2}\left(\frac{M}{3}\right)v^2 = \frac{\Delta M c^2}{3}$

Multiply both sides by $3$:

$\frac{1}{2} M v^2 = \Delta M c^2$

Thus,

$v^2 = \frac{2\Delta M c^2}{M}$

$v = c\sqrt{\frac{2\Delta M}{M}}$

5. Match with options

This matches Option C:

$\boxed{c\sqrt{\frac{2\Delta M}{M}}}$