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

Question

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 \(n = 8\).