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Question
Use a number line or your Desmos calculator for this problem.

*You will want to hold down the ctrl key when clicking on the Desmos link, so you don't lose your place in this test.

(1 point)
The √40 is between
and
.

Answer 1

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 \(\text{7}\).