Question

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

8

12.5
12.5

16
16

18

Answer 1

To solve the inequality \(\sqrt{2n} < 5\), we will follow these steps:

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

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

Now, we need to find which of the provided values for \(n\) makes the inequality true:

- For \(n = 8\):
\[
8 < 12.5 \quad \text{(true)}
\]

- For \(n = 12.5\):
\[
12.5 < 12.5 \quad \text{(false)}
\]

- For \(n = 16\):
\[
16 < 12.5 \quad \text{(false)}
\]

- For \(n = 18\):
\[
18 < 12.5 \quad \text{(false)}
\]

The only value from the options provided that makes the inequality \(\sqrt{2n} < 5\) true is \(n = 8\).