Given:
The objective is to find the correct pair of radical expressions from the given options.
Let's check with option (A).
![\begin{gathered} \sqrt[]{45}=\sqrt[]{3*3*5} \\ =3\sqrt[]{5} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/gm0ylk50wgeh50un4q2yyq5lk44uxodmop.png)
Thus, option (A) is wrong.
Let's check with option (B).
![\begin{gathered} \sqrt[]{75}=\sqrt[]{3*5*5} \\ =5\sqrt[]{3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/tn4prd4rorafqgzr6trs43pkm821vo7bj5.png)
Thus, option (B) is wrong.
Let's check with option (C).
![\begin{gathered} \sqrt[]{54}=\sqrt[]{3*3*3*2} \\ =3\sqrt[]{6} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ngd6j65k3461tov7j7e0kees85sbspwt4y.png)
Thus, option (C) is wrong.
Let's check with option (D).
![\begin{gathered} \sqrt[]{180}=\sqrt[]{3*3*2*2*5} \\ =3\sqrt[]{2*2*5} \\ =3\sqrt[]{20} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/4ek3al9waz8in0u8z31jlpmhv2e7u939dk.png)
Thus, option (D) is correct,
Hence, option (D) is a pair of equivalent radical expressions.