Question

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

$\sqrt{5}$ is between $2$ and $3$, we can write it as $2<\sqrt{5}<3$.

Step3: Multiply the inequality by 6

Multiply each part of the inequality $2<\sqrt{5}<3$ by $6$. We get $6\times2 < 6\sqrt{5}<6\times3$, which simplifies to $12 < 6\sqrt{5}<18$.

Answer:

For the first blank: 2
For the second blank: 3
For the third blank: 2 and 3
For the fourth blank: 12
For the fifth blank: 18