To determine between which pair of rational numbers \( \sqrt{18} \) lies, we first calculate \( \sqrt{18} \).
We know that:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]
Next, we need to approximate \( \sqrt{2} \). The approximate value of \( \sqrt{2} \) is about 1.414. Thus:
\[ \sqrt{18} \approx 3 \times 1.414 \approx 4.242 \]
Now, we can analyze the provided options to see where \( 4.242 \) lies:
- Between 4.2 and 4.3
- 4.2 < 4.242 < 4.3 ✅
- Between 9 and 9.2
- 9 < 4.242 < 9.2 ❌
- Between 4.3 and 4.5
- 4.3 < 4.242 < 4.5 ❌
- Between 8.9 and 9.1
- 8.9 < 4.242 < 9.1 ❌
The correct answer is:
Between 4.2 and 4.3.
1 answer