To determine between which pair of rational numbers \( \sqrt{18} \) lies, we first need to calculate \( \sqrt{18} \).
We know that: \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \] Now we need to find the approximate value of \( \sqrt{2} \). The approximate value is: \[ \sqrt{2} \approx 1.414 \] Thus, we can calculate \( \sqrt{18} \): \[ \sqrt{18} \approx 3 \times 1.414 \approx 4.242 \]
Now, we will identify between which pairs of rational numbers \( 4.242 \) falls:
- Between 4.2 and 4.3: \( 4.2 < 4.242 < 4.3 \) (True)
- Between 8.9 and 9.1: \( 8.9 < 4.242 < 9.1 \) (False)
- Between 9 and 9.2: \( 9 < 4.242 < 9.2 \) (False)
- Between 4.3 and 4.5: \( 4.3 < 4.242 < 4.5 \) (False)
Therefore, the correct response is: Between 4.2 and 4.3.