Problem 108

The value of $\sqrt{36}$ is
$6$ and the value of $\sqrt{49}=7$. Since $37$ is greater than $36$ and less than $49$, then $\sqrt{37}$ lies between $6$ and $7$. Since $37$ is much closer to $36$ than it is to $49$, then of the given answers, the value
of $\sqrt{37}$ is closest to $6$.

More precisely, $6.5^2=42.25$ and
$\text{37 lt;42.25}$, so $\text{37 lt;6.5}$.