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

Question

true?(1 point)
Responses

12.5
12.5

16
16

18
18

8

Answer 1

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

\[ 2n < 25 \]

Next, divide both sides by 2:

\[ n < 12.5 \]

Now let's check the response options:

1. 12.5: This does not satisfy the inequality since \( n \) must be less than 12.5.
2. 16: This does not satisfy the inequality since \( 16 \) is greater than \( 12.5 \).
3. 18: This does not satisfy the inequality since \( 18 \) is greater than \( 12.5 \).
4. 8: This satisfies the inequality since \( 8 < 12.5 \).

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