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? \( \begin{array}{ll}\text { A } n \geq 7 & \text { B } n \leq-7 \\ \text { C } n \geq 0 & \text { D } n \leq 0\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
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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