Question

I inserted a picture of the question, can you please make it very short CHECK ALL THAT APPLY

Answer 1

We have the following expression:

`3\sqrt[]{6}`

since

`\sqrt[]{9}=3`

Our expression is equivalent to

`\sqrt[]{9}\cdot\sqrt[]{6}`

Additionally, we can note that

`\sqrt[]{6}=\sqrt[]{2*3}=\sqrt[]{2}\cdot\sqrt[]{3}`

Then, we can write

`\begin{gathered} \sqrt[]{9}\cdot\sqrt[]{6}=\sqrt[]{9}\cdot\sqrt[]{2}\cdot\sqrt[]{3} \\ \text{which is equivalent to} \\ \sqrt[]{9\cdot3}\cdot\sqrt[]{2}=\sqrt[]{27}\cdot\sqrt[]{2} \end{gathered}`

And finally, we can note that

`\sqrt[]{27}\cdot\sqrt[]{2}=\sqrt[]{27*2}=\sqrt[]{54}`

Therefore, the answers are:

`\begin{gathered} \sqrt[]{9}\cdot\sqrt[]{6} \\ \\ \sqrt[]{27}\cdot\sqrt[]{2} \\ \\ \sqrt[]{54} \end{gathered}`