Given:
The objective is to find the correct pair of radical expressions from the given options.
Let's check with option (A).
[tex]\begin{gathered} \sqrt[]{45}=\sqrt[]{3\times3\times5} \\ =3\sqrt[]{5} \end{gathered}[/tex]Thus, option (A) is wrong.
Let's check with option (B).
[tex]\begin{gathered} \sqrt[]{75}=\sqrt[]{3\times5\times5} \\ =5\sqrt[]{3} \end{gathered}[/tex]Thus, option (B) is wrong.
Let's check with option (C).
[tex]\begin{gathered} \sqrt[]{54}=\sqrt[]{3\times3\times3\times2} \\ =3\sqrt[]{6} \end{gathered}[/tex]Thus, option (C) is wrong.
Let's check with option (D).
[tex]\begin{gathered} \sqrt[]{180}=\sqrt[]{3\times3\times2\times2\times5} \\ =3\sqrt[]{2\times2\times5} \\ =3\sqrt[]{20} \end{gathered}[/tex]Thus, option (D) is correct,
Hence, option (D) is a pair of equivalent radical expressions.
