Question
Between which pair of rational numbers on a number line does √18 lie?
(1 point)
A. Between 4.2 and 4.3
B. Between 9 and 9.2
C. Between 8.9 and 9.1
D. Between 4.3 and 4.5
(1 point)
A. Between 4.2 and 4.3
B. Between 9 and 9.2
C. Between 8.9 and 9.1
D. Between 4.3 and 4.5
Answers
GPT-4o mini
To determine between which pair of rational numbers \(\sqrt{18}\) lies, we first need to approximate \(\sqrt{18}\).
We know that:
\[
\sqrt{16} = 4
\]
\[
\sqrt{25} = 5
\]
Since \(16 < 18 < 25\), it follows that:
\[
4 < \sqrt{18} < 5
\]
Next, we can refine this approximation. Since \(18\) is closer to \(16\) and \(25\), we can check \(4.2\) and \(4.3\):
Calculating \(4.2^2\):
\[
4.2^2 = 17.64
\]
Calculating \(4.3^2\):
\[
4.3^2 = 18.49
\]
Now we see that:
\[
4.2^2 < 18 < 4.3^2
\]
This means that \(\sqrt{18}\) is between \(4.2\) and \(4.3\).
Thus, the answer is:
**A. Between 4.2 and 4.3**.
We know that:
\[
\sqrt{16} = 4
\]
\[
\sqrt{25} = 5
\]
Since \(16 < 18 < 25\), it follows that:
\[
4 < \sqrt{18} < 5
\]
Next, we can refine this approximation. Since \(18\) is closer to \(16\) and \(25\), we can check \(4.2\) and \(4.3\):
Calculating \(4.2^2\):
\[
4.2^2 = 17.64
\]
Calculating \(4.3^2\):
\[
4.3^2 = 18.49
\]
Now we see that:
\[
4.2^2 < 18 < 4.3^2
\]
This means that \(\sqrt{18}\) is between \(4.2\) and \(4.3\).
Thus, the answer is:
**A. Between 4.2 and 4.3**.