Question

use the drop - down menus to complete each statement to show why $6sqrt{5}$ is between 12 and 18. $4 < 5 < 9$, so $sqrt{5}$ is between and. this means that $sqrt{5}$ is between $sqrt{2}$ and $sqrt{3}$. so, $6sqrt{5}$ is between and.

Explanation:

Step1: Find square - root bounds of 5

Since \(4 < 5<9\), and \(\sqrt{4} = 2\), \(\sqrt{9}=3\), so \(\sqrt{5}\) is between \(2\) and \(3\).

Step2: Multiply the bounds by 6

If \(\sqrt{5}\) is between \(2\) and \(3\), then \(6\sqrt{5}\) is between \(6\times2\) and \(6\times3\).
\(6\times2 = 12\) and \(6\times3=18\).

Answer:

For the first two blanks: 2, 3; for the last two blanks: 12, 18.