1) First notice that we have the following expressions that are always true:
![\begin{gathered} \sqrt[]{36}=6 \\ \sqrt[]{49}=7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/5s208pceczmtnu6a2520jmje9784d0t5so.png)
We also know that:

Using square root on the whole equality we get:
![\begin{gathered} \sqrt[]{36}<\sqrt[]{39}<\sqrt[]{49} \\ \Rightarrow6<\sqrt[]{39}<7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/6hxn1ebdoc6qirpd6shu96dqqs8gau965t.png)
therefore, the square root of 39 is between 6 and 7.
2)for the square root of 600, we have the following:
![\begin{gathered} 600<625 \\ \text{ using square root on both sides:} \\ \sqrt[]{600}<\sqrt[]{625}=25 \\ \Rightarrow\sqrt[]{600}<25 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/fe71250zl4178befum6ijes5mjd63xyx8t.png)
since the square root of 625 is the minimum number that has an integer as a solution, we have that the square root of 600 is between 24 and 25