#### Answer

the value must be between $3$ and $4$

#### Work Step by Step

The value of $\sqrt{13}$ is definitely not equal to $5.7,$ because $5.7^2$ is greater than $5^2$ (which is equal to $25.$) This not close to $13.$ Also, the value of $\sqrt{13}$ is between the value of $\sqrt{9}$ and $\sqrt{16}$. So the value of $\sqrt{13}$ must be between $3$ and $4.$