Question

Enter the correct answer in the box. It’s in the picture I attached

Answer 1

Given:

`7\sqrt[]{28x^6}+4\sqrt[]{7x^6}`

We will simplify the given expression as follows:

Note the following:

`\begin{gathered} x^6=(x^3)^2 \\ 28=4*7=2^2*7 \end{gathered}`

So,

`\begin{gathered} 7\sqrt[]{28x^6}=7\cdot\sqrt[]{2^2\cdot7\cdot(x^3)^2}=7\cdot2\cdot x^3\cdot\sqrt[]{7}=14x^3\sqrt[]{7} \\ 4\sqrt[]{7x^6}=4\sqrt[]{7(x^3)^2}=4x^3\sqrt[]{7} \end{gathered}`

so, the value of the given expression will be:

`7\sqrt[]{28x^6}+4\sqrt[]{7x^6}=14x^3\sqrt[]{7}+4x^3\sqrt[]{7}=18x^3\sqrt[]{7}`

So, the answer will be:

`18x^3\sqrt[]{7}`