To find the square root of 40 (\(\sqrt{40}\)), we can first simplify it:
\[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \]
Next, we need to approximate \(\sqrt{10}\):
- \(\sqrt{9} = 3\) (since \(3^2 = 9\))
- \(\sqrt{16} = 4\) (since \(4^2 = 16\))
Thus, \(\sqrt{10}\) is between 3 and 4. To get a better estimate, we can consider that \(\sqrt{10} \approx 3.16\) (more accurate value).
Now substituting back:
\[ 2\sqrt{10} \approx 2 \times 3.16 \approx 6.32 \]
Therefore, \(\sqrt{40}\) is approximately \(6.32\).
To find two perfect squares between which \(\sqrt{40}\) falls:
- Since \(6^2 = 36\)
- And \(7^2 = 49\)
Thus, \( \sqrt{40} \) is between \(6\) and \(7\).
So, we conclude that:
\(\sqrt{40}\) is between \(\text{6}\) and \(\text{7}\).
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