Which of the following values for n makes the inequality 2n−−√<5 true?(1 point)

Answer 1

To solve the inequality \( \sqrt{2n} < 5 \), we can start by squaring both sides to eliminate the square root. However, we must ensure that both sides are non-negative when doing so.

1. Start with the inequality: \[ \sqrt{2n} < 5 \]

2. Square both sides: \[ 2n < 25 \]

3. Now, divide both sides by 2 to isolate \( n \): \[ n < \frac{25}{2} \] \[ n < 12.5 \]

Thus, the inequality \( \sqrt{2n} < 5 \) is true for values of \( n \) that are less than 12.5.

If you want a specific integer or natural number value for \( n \), any integer less than or equal to 12 would satisfy this inequality (e.g., \( n = 0, 1, 2, \ldots, 12 \)).