Question

Help with this please

Answer 1

Consider the given radical,

`\sqrt[]{128}`

Factorize the number,

`128=2^7`

Consider the following properties,

`\begin{gathered} a^(m+1)=a^m* a \\ a^(mn)=(a^m)^n \end{gathered}`

Then the radical can be simplified as,

`\sqrt[]{128}=\sqrt[]{2^7}=\sqrt[]{2^6*2}=\sqrt[]{64*2}=\sqrt[]{64}*\sqrt[]{2}`

Thus, the radical is simplified as,

`\sqrt[]{128}=\sqrt[]{64}*\sqrt[]{2}=8\sqrt[]{2}`