Question

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

8
8

16
16

12.5
12.5

18

Answer 1

To solve the inequality \( \sqrt{2n} < 5 \), we first isolate \( n \):

1. Square both sides to eliminate the square root:
\[
2n < 25
\]

2. Divide both sides by 2:
\[
n < 12.5
\]

Now we can check the values provided:

- \( n = 8 \): \( 8 < 12.5 \) (True)
- \( n = 16 \): \( 16 < 12.5 \) (False)
- \( n = 12.5 \): \( 12.5 < 12.5 \) (False)
- \( n = 18 \): \( 18 < 12.5 \) (False)

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