Donnelly Powers
08/15/2023 · Elementary School

2. What is the condition on the variable in \( 2 \sqrt{-7 n} \) for the radicand to be a real number? \( \begin{array}{ll}\text { A } n \geq 7 & \text { B } n \leq-7 \\ \text { C } n \geq 0 & \text { D } n \leq 0\end{array} \)

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To determine the condition on the variable \( n \) for the expression \( 2 \sqrt{-7n} \) to be a real number, we need to analyze the radicand, which is \( -7n \). For the square root to yield a real number, the radicand must be non-negative: \[ -7n \geq 0 \] To solve this inequality, we can divide both sides by -7. Remember that when we divide or multiply an inequality by a negative number, we must reverse the inequality sign: \[ n \leq 0 \] Thus, the condition on \( n \) for \( 2 \sqrt{-7n} \) to be a real number is: \[ \boxed{D} \quad n \leq 0 \]

Quick Answer

\( n \leq 0 \) Therefore, the correct answer is D. \( n \leq 0 \)
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