Question

Not a timed or graded assignment. Need full work shown. Quick answer with work = amazing review

Answer 1

The Solution:

Given the expression below:

`10\text{ }\sqrt[]{112m^6}`

We are asked to simplified in radical form.

Let's find the factors of 112.

`\begin{gathered} 112=2*56 \\ =2*2*28 \\ =2*2*2*14 \\ =2*2*2*2*7 \end{gathered}`
`\sqrt[]{m^6}=\sqrt[]{m^3* m^3}`

So,

`\sqrt[]{112m^6}=\sqrt[]{112* m^3* m^3}=\sqrt[]{2*2*2*2*7* m^3* m^3}`

`10\sqrt[]{112m^6}=10\sqrt[]{2*2*2*2*7* m^3* m^3}=10(2*2* m^3)\text{ }\sqrt[]{7}`

Thus,

`10\sqrt[]{112m^6}=\text{ }10(2*2* m^3)\text{ }\sqrt[]{7}=10(4)m^3\text{ }\sqrt[]{7}=40m^3\text{ }\sqrt[]{7}`

Therefore, the correct answer is

`40m^3\text{ }\sqrt[]{7}`