Question

Determine whether the statement is true or false. Iftrue, explain why. If false, provide a counterexample.

Answer 1

Given:

`\sqrt[]{x+y}`

Let

`\sqrt[]{x+y}=\sqrt[]{x}+\sqrt[]{y}`

So square of both side is:

`\begin{gathered} \sqrt[]{x+y}=\sqrt[]{x}+\sqrt[]{y} \\ \text{squre f both side:} \\ (\sqrt[]{x+y})^2=(\sqrt[]{x}+√(y))^2 \\ x+y=x+y+2\sqrt[]{xy} \end{gathered}`

Here :

`\sqrt[]{x+y}\\e\sqrt[]{x}+\sqrt[]{y}`

So the given statement is is false.