Given:
[tex]7\sqrt[]{28x^6}+4\sqrt[]{7x^6}[/tex]
We will simplify the given expression as follows:
Note the following:
[tex]\begin{gathered} x^6=(x^3)^2 \\ 28=4\times7=2^2\times7 \end{gathered}[/tex]
So,
[tex]\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}[/tex]
so, the value of the given expression will be:
[tex]7\sqrt[]{28x^6}+4\sqrt[]{7x^6}=14x^3\sqrt[]{7}+4x^3\sqrt[]{7}=18x^3\sqrt[]{7}[/tex]
So, the answer will be:
[tex]18x^3\sqrt[]{7}[/tex]
