Question
witch numberline showes the aproxemet location of the root of 24
Answers
Answered by
GPT-4o mini
To approximate the location of the square root of 24 on a number line, we can first determine the square roots of the perfect squares close to 24.
- The square root of 16 is 4 (since \(4^2 = 16\)).
- The square root of 25 is 5 (since \(5^2 = 25\)).
Since \(24\) is between \(16\) and \(25\), we know that:
\[
4 < \sqrt{24} < 5
\]
Next, we can further refine our estimate.
- \(\sqrt{24}\) can be simplified as \(\sqrt{4 \times 6} = 2\sqrt{6}\).
- Since \(\sqrt{6} \approx 2.45\), we have \(2\sqrt{6} \approx 4.9\).
Thus:
\[
4.8 < \sqrt{24} < 5
\]
To visualize this on a number line, you would place points at 4.8 and 5, and mark the approximate location of \(\sqrt{24}\) a bit closer to 5, around 4.9.
So, \(\sqrt{24}\) is approximately 4.9 on the number line.
- The square root of 16 is 4 (since \(4^2 = 16\)).
- The square root of 25 is 5 (since \(5^2 = 25\)).
Since \(24\) is between \(16\) and \(25\), we know that:
\[
4 < \sqrt{24} < 5
\]
Next, we can further refine our estimate.
- \(\sqrt{24}\) can be simplified as \(\sqrt{4 \times 6} = 2\sqrt{6}\).
- Since \(\sqrt{6} \approx 2.45\), we have \(2\sqrt{6} \approx 4.9\).
Thus:
\[
4.8 < \sqrt{24} < 5
\]
To visualize this on a number line, you would place points at 4.8 and 5, and mark the approximate location of \(\sqrt{24}\) a bit closer to 5, around 4.9.
So, \(\sqrt{24}\) is approximately 4.9 on the number line.