Question

Which of the following is equivalent to the radical expression below when x is greater than or equal to 7

Answer 1

SOLUTION

The radical expression given is

$\sqrt[]{x-7}.\sqrt[]{x+1}$

Applying the rule

$\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{ab}$

We obtain

$\sqrt[]{x-7}\times\sqrt[]{x+1}=\sqrt[]{(x-7)(x+1)}$

Expanding the parenthesis, we have

$\begin{gathered} \sqrt[]{(x(x+1)-7(x+1)} \\ =\sqrt[]{x^2+x-7x-7} \\ =\sqrt[]{x^2-6x-7} \end{gathered}$

The radical expression is equivalent to

$\sqrt[]{x^2-6x-7}$

The right option is A