The Solution:
Given the expression below:
[tex]10\text{ }\sqrt[]{112m^6}[/tex]
We are asked to simplified in radical form.
Let's find the factors of 112.
[tex]\begin{gathered} 112=2\times56 \\ =2\times2\times28 \\ =2\times2\times2\times14 \\ =2\times2\times2\times2\times7 \end{gathered}[/tex][tex]\sqrt[]{m^6}=\sqrt[]{m^3\times m^3}[/tex]
So,
[tex]\sqrt[]{112m^6}=\sqrt[]{112\times m^3\times m^3}=\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}[/tex]
[tex]10\sqrt[]{112m^6}=10\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}=10(2\times2\times m^3)\text{ }\sqrt[]{7}[/tex]
Thus,
[tex]10\sqrt[]{112m^6}=\text{ }10(2\times2\times m^3)\text{ }\sqrt[]{7}=10(4)m^3\text{ }\sqrt[]{7}=40m^3\text{ }\sqrt[]{7}[/tex]
Therefore, the correct answer is
[tex]40m^3\text{ }\sqrt[]{7}[/tex]
