Question

Which of the following is a pair of equivalent radical expressions?A745 and 3/15B.775 and 375154 and 9V6180 and 3/20

Answer 1

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}`

Thus, option (A) is wrong.

Let's check with option (B).

`\begin{gathered} \sqrt[]{75}=\sqrt[]{3*5*5} \\ =5\sqrt[]{3} \end{gathered}`

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}`

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}`

Thus, option (D) is correct,

Hence, option (D) is a pair of equivalent radical expressions.