To approximate the location of \( \sqrt{48} \), we first note that \( 48 \) can be simplified as follows:
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
Next, we need to approximate \( \sqrt{3} \). The value of \( \sqrt{3} \) is approximately \( 1.732 \). Therefore, we can approximate:
\[ \sqrt{48} \approx 4 \times 1.732 = 6.928 \]
Thus, the approximate value of \( \sqrt{48} \) is about \( 6.9 \).
On a number line, \( \sqrt{48} \) is located just below \( 7 \) since \( 6.928 \) is very close to \( 7 \) but not quite there. Therefore, you would look for a point slightly before \( 7 \) on the number line to indicate the approximate location of \( \sqrt{48} \).
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