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

Question

2
𝑛
<
5
true?(1 point)
Responses

16
16

8
8

18
18

12.5

Answer 1

To solve the inequality \( \sqrt{2n} < 5 \), we'll first square both sides to eliminate the square root:

\[ 2n < 25 \]

Now, divide both sides by 2:

\[ n < 12.5 \]

So, the values of \( n \) that satisfy the inequality must be less than 12.5. Now let's evaluate the options:

• 16: \( 16 \) is not less than \( 12.5 \).
• 8: \( 8 \) is less than \( 12.5 \) (valid).
• 18: \( 18 \) is not less than \( 12.5 \).
• 12.5: \( 12.5 \) is not less than \( 12.5 \).

Therefore, the only value for \( n \) that satisfies the inequality \( \sqrt{2n} < 5 \) is 8.