40−−√ is between what and what.

1 answer

To find the square root of 40 (\(\sqrt{40}\)), we can look for two perfect squares between which 40 lies.

We know:

  • \(6^2 = 36\)
  • \(7^2 = 49\)

Thus, \(36 < 40 < 49\), which implies:

\[ 6 < \sqrt{40} < 7 \]

Now, let's compute \(\sqrt{40}\) more precisely. We can break it down as follows:

\(\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}\).

To estimate \(\sqrt{10}\), we can see:

  • \(3^2 = 9\)
  • \(4^2 = 16\)

Thus, \(3 < \sqrt{10} < 4\), leading to:

\[ 6 < \sqrt{40} < 8 \]

Therefore, \(\sqrt{40}\) is between 6 and 7.

So, the final answer is:

\(\sqrt{40}\) is between 6 and 7.