Two nuclei have mass numbers in the ratio $27:125$. The ratio of their nuclear radii would be:

Here ,

 $\begin{array}{l}{A}_1:A_2=27:125\\ \Rightarrow \frac{A_1}{A_2}=\frac{27}{125}\end{array}$

Since,  $R=R_0{A}^{1/3}$

 $\begin{array}{l}\therefore \frac{R_1}{R_2}=\frac{A_1^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{A_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}={\left(\frac{A_1}{A_2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\\ ={\left(\frac{27}{125}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\\ =\frac{3}{5}\end{array}$

 $\therefore$  The ratio of their radii = 3 : 5