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

Which of the following is equivalent to the radical expression below when x is greater-example-1
User Cudos
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1 Answer

4 votes

SOLUTION

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

User KJ Tsanaktsidis
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