Question

what is the side length of a square with an area of 52 square units? units² is between 49 and 64 units². so, between which two whole numbers is √52? √52 units area = 52 units² √52 units is between the whole numbers

Explanation:

Step1: Recall area - side - length relation

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 52$, then $s=\sqrt{52}$.

Step2: Find perfect - square bounds

We know that $7^{2}=49$ and $8^{2}=64$. Since $49<52<64$, we have $\sqrt{49}<\sqrt{52}<\sqrt{64}$, which simplifies to $7 < \sqrt{52}<8$.

Answer:

7 and 8