Question

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

Answer 1

The radical expression given is

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

Applying the rule

`\sqrt[]{a}*\sqrt[]{b}=\sqrt[]{ab}`

We obtain

`\sqrt[]{x-7}*\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