SOLUTION
The radical expression given is
[tex]\sqrt[]{x-7}.\sqrt[]{x+1}[/tex]
Applying the rule
[tex]\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{ab}[/tex]
We obtain
[tex]\sqrt[]{x-7}\times\sqrt[]{x+1}=\sqrt[]{(x-7)(x+1)}[/tex]
Expanding the parenthesis, we have
[tex]\begin{gathered} \sqrt[]{(x(x+1)-7(x+1)} \\ =\sqrt[]{x^2+x-7x-7} \\ =\sqrt[]{x^2-6x-7} \end{gathered}[/tex]
The radical expression is equivalent to
[tex]\sqrt[]{x^2-6x-7}[/tex]
The right option is A
