===============================================
Explanation:
When you list out the perfect squares, notice that 49 and 64 are on that list.
These are values we focus on because 49 < 52 < 64
We'll apply the square root to all three sides
[tex]49 < 52 < 64\\\\\sqrt{49} < \sqrt{52} < \sqrt{64}\\\\7 < \sqrt{52} < 8\\\\[/tex]
This shows that [tex]\sqrt{52}[/tex] is between 7 and 8
A calculator helps confirm this
[tex]\sqrt{52} \approx 7.2111\\\\[/tex]
