Given,

Volume of a cube = 474.552 cubic metres

V = 8³,

S = side of the cube

So,

8³ = 474.552 cubic metres

= 8 =

On factorising 474552 into prime factors, we get:

474552 = 2×2×2×3×3×3×13×13×13

On grouping the factors in triples of equal factors, we get:

474552 = {2×2×2}×{3×3×3}×{13×13×13}

Now taking 1 factor from each group we get,

Also,

So, length of the side is 7.8m.