Answer:
[tex]x\ge-2[/tex]Explanation: The product has two square-roots being multipled together, the inside of each of the root must be greater than or equal to zero, this in Mathematics can be written as follows:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \end{gathered}[/tex]Therefore, applying the condition leads us to the following conclusion:
[tex]\begin{gathered} \sqrt[]{x-5}\times\sqrt[]{x+2} \\ \therefore\rightarrow \\ x-5\ge0\rightarrow x\ge5 \\ x+2\ge0\rightarrow x\ge-2 \end{gathered}[/tex]
Therefore it follows that x must be:
[tex]x\ge-2[/tex]
