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

Question

8
16
18
12.5

Answer 1

To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides to eliminate the square root (as long as we know both sides are non-negative):

\[ 2n < 25 \]

Next, we divide both sides by 2 to isolate \( n \):

\[ n < 12.5 \]

Now we can evaluate the options given:

• 8: \( 8 < 12.5 \) (True)
• 16: \( 16 < 12.5 \) (False)
• 18: \( 18 < 12.5 \) (False)
• 12.5: \( 12.5 < 12.5 \) (False)

The only value for \( n \) that makes the inequality true is:

8.