Dimensional Homogeneity:

When the dimensions of each terms in an equation on both sides are equal it refers to dimensional homogeneity

Thus we can say that if the dimensions of each term on both sides of an equation are same then the equation is known as the dimensionally homogeneous equation.

The power of fundamental dimensions (l,m,t) on both sides of the equation will be identical for a dimensionally homogenous equation

Let us consider

V=$\sqrt{2gh}$

L.H.S =V=$\frac{L}{T}$=

=LT$^{-1}$

R.H.S=$\sqrt{2gH}$

=$\sqrt{\frac{L}{T^{2}}\times l}$

=${\sqrt\frac{L^{2}}{T^{2}}}=\frac{L}{T}$

=$LT^{-1}$

Dimensions of L.H.S = Dimensions of R.H.S

LT$^{-1}$ = LT$^{-1}$

Equation V=$\sqrt{2gh}$ is dimensionally homogenous