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:

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

Here :

$\sqrt[]{x+y}\ne\sqrt[]{x}+\sqrt[]{y}$

So the given statement is is false.