To find between which pair of rational numbers \( \sqrt{18} \) lies, we can first determine the approximate value of \( \sqrt{18} \).
The value of \( \sqrt{18} \) can be simplified as follows:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \]
Now, since \( \sqrt{2} \) is approximately 1.414, we can find:
\[ 3\sqrt{2} \approx 3 \times 1.414 \approx 4.242 \]
So, \( \sqrt{18} \approx 4.242 \).
Now, we compare this value to the given options:
- Between 4.3 and 4.5: 4.242 is less than 4.3, so this option is not correct.
- Between 9 and 9.2: 4.242 is much less than both 9 and 9.2, so this option is not correct.
- Between 4.2 and 4.3: 4.242 is greater than 4.2 and less than 4.3, so this option is correct.
- Between 8.9 and 9.1: Again, 4.242 is much less than both 8.9 and 9.1, so this option is not correct.
Thus, the correct answer is:
Between 4.2 and 4.3.
1 answer