To solve the inequality \( \sqrt{2n} < 5 \), we can start by squaring both sides to eliminate the square root (provided \( 2n \geq 0 \) which we assume since \( n \) is typically expected to be a non-negative value).
Starting with:
\[ \sqrt{2n} < 5 \]
Squaring both sides:
\[ 2n < 25 \]
Now, we can solve for \( n \):
\[ n < \frac{25}{2} \] \[ n < 12.5 \]
Now we can evaluate the response options:
- \( n = 16 \): Not valid, since \( 16 > 12.5 \)
- \( n = 12.5 \): Not valid, since \( 12.5 \) equals \( 12.5 \), not less than.
- \( n = 8 \): Valid, since \( 8 < 12.5 \)
- \( n = 18 \): Not valid, since \( 18 > 12.5 \)
The only value for \( n \) that satisfies the inequality \( \sqrt{2n} < 5 \) is \( \boxed{8} \).