To determine which of the given values for \( n \) makes the inequality \( \sqrt{2n} < 5 \) true, we can solve the inequality step by step.
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Start with the inequality: \[ \sqrt{2n} < 5 \]
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Square both sides to eliminate the square root (this is valid since both sides are positive): \[ 2n < 25 \]
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Divide both sides by 2: \[ n < 12.5 \]
Now, we will check each of the provided values for \( n \):
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For \( n = 8 \): \[ 8 < 12.5 \quad \text{(True)} \]
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For \( n = 16 \): \[ 16 < 12.5 \quad \text{(False)} \]
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For \( n = 12.5 \): \[ 12.5 < 12.5 \quad \text{(False)} \]
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For \( n = 18 \): \[ 18 < 12.5 \quad \text{(False)} \]
The only value that satisfies the inequality \( \sqrt{2n} < 5 \) is \( n = 8 \).
Thus, the correct answer is: 8
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