To locate \(\sqrt{48}\) on a number line, we need to first simplify \(\sqrt{48}\):
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
Next, we need to estimate \(\sqrt{3}\). We know that:
- \(\sqrt{3} \approx 1.732\)
Now, we can approximate \(\sqrt{48}\):
\[ \sqrt{48} \approx 4 \times 1.732 \approx 6.928 \]
Now we know that \(\sqrt{48}\) is approximately \(6.928\).
To place this value on a number line, note the whole numbers around it:
- \(6^2 = 36\)
- \(7^2 = 49\)
This means \(\sqrt{48}\) is between \(6\) and \(7\), closer to \(7\).
Thus, when drawing or marking on a number line:
- Draw a horizontal line.
- Mark points for \(6\) and \(7\).
- Estimate and mark a point slightly less than \(7\), around \(6.9\), which represents \(\sqrt{48}\).
This gives you the approximate location of \(\sqrt{48}\) on a number line.