Given:
The given radical expression is,
[tex]\sqrt{x-7}\cdot\sqrt{x+1}[/tex]
Required:
To find the expression equivalent to the given radical expression when
[tex]x>7[/tex]
Explanation:
Let us solve the given expression.
[tex]\begin{gathered} \sqrt{x-7}\cdot\sqrt{x+1} \\ =\sqrt{(x-7)\cdot(x+1)} \\ =\sqrt{x^2+x-7x-7} \\ =\sqrt{x^2-6x-7} \end{gathered}[/tex]
Final Answer:
The expression equivalent to the given radical expression when
[tex]x>7[/tex]
is given by,
[tex]\sqrt{x^2-6x-7}[/tex]
Option D is correct.
