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. so, $6sqrt{5}$ is between and.

Explanation:

Step1: Analyze square - root range

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

Step2: Multiply by 6

If $\sqrt{5}$ is between $2$ and $3$, then when we multiply by $6$, we get $6\times2<6\sqrt{5}<6\times3$.

Step3: Calculate the bounds

$6\times2 = 12$ and $6\times3=18$, so $6\sqrt{5}$ is between $12$ and $18$.

Answer:

The first two blanks: $2$, $3$; the last two blanks: $12$, $18$