To solve the inequality \( \sqrt{2n} < 5 \), we can start by squaring both sides to eliminate the square root. However, it’s crucial to ensure that both sides are non-negative before squaring.
-
Square both sides: \[ 2n < 25 \]
-
Divide by 2: \[ n < 12.5 \]
Now that we have the condition \( n < 12.5 \), let's check the provided options:
-
8: This satisfies \( n < 12.5 \).
-
16: This does NOT satisfy \( n < 12.5 \).
-
18: This does NOT satisfy \( n < 12.5 \).
-
12.5: This does NOT satisfy \( n < 12.5 \) since the inequality is strict.
Thus, the only value that makes the inequality \( \sqrt{2n} < 5 \) true is:
8