Question

Which choice is equivalent to the quotient below? sqrt 7/8* sqrt7/187/16/121/23/47/12

Answer 1

We can apply the following properties of radicals:

`\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{(a)/(b)}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}`

Then, we have:

`\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{(7)/(8)}\cdot\sqrt[]{(7)/(18)}=\sqrt[]{(7)/(8)\cdot(7)/(18)} \\ \sqrt[]{(7)/(8)}\cdot\sqrt[]{(7)/(18)}=\sqrt[]{(7\cdot7)/(8\cdot18)} \\ \sqrt[]{(7)/(8)}\cdot\sqrt[]{(7)/(18)}=\sqrt[]{(49)/(144)} \\ \text{ Apply the quotient property} \\ \sqrt[]{(7)/(8)}\cdot\sqrt[]{(7)/(18)}=\frac{\sqrt[]{49}}{\sqrt[]{144}} \\ \sqrt[]{(7)/(8)}\cdot\sqrt[]{(7)/(18)}=(7)/(12) \end{gathered}`

Therefore, the choice that is equivalent to the given product is:

`(7)/(12)`