Question

Please help my session keeps getting ended unexpectedly they say

Answer 1

The initial expression is

`\sqrt[]{(16x^4y^8)/(5z)}`

This can be simplified as shown below

`\begin{gathered} \sqrt[]{(16x^4y^8)/(5z)}=\frac{\sqrt[]{16x^4y^8}}{\sqrt[]{5z}} \\ =\frac{\sqrt[]{16}\sqrt[]{x^4}\sqrt[]{y^8_{}}}{_{}\sqrt[]{5}\sqrt[]{z}} \\ =\frac{4x^2y^4}{\sqrt[]{5}\sqrt[]{z}} \end{gathered}`

Now, we need to rationalize the denominator. First, we need to multiply the simplified expression by 1

`\begin{gathered} \Rightarrow\sqrt[]{(16x^4y^8)/(5z)}=\frac{4x^2y^4_{}}{\sqrt[]{5z}}\cdot1=\frac{4x^2y^4_{}}{\sqrt[]{5z}}\cdot\frac{\sqrt[]{5z}}{\sqrt[]{5z}}=\frac{4x^2y^4\sqrt[]{5z}}{5z} \\ \Rightarrow\sqrt[]{(16x^4y^8)/(5z)}=\frac{4x^2y^4\sqrt[]{5z}}{5z} \end{gathered}`

We can modify how the final expression looks like, but this is the answer.

The answer is (4x^2y^4sqrt(5z))/5z