To approximate the square root of $76$, we can start by identifying the two perfect squares closest to $76$ and see where it lies between them.

Here are the squares of whole numbers near $76$:

1. $6^2 = 36$
2. $7^2 = 49$
3. $8^2 = 64$
4. $9^2 = 81$
5. $10^2 = 100$

From this, we can observe that:

• $76$ lies between $8^2 = 64$ and $9^2 = 81$.
• Therefore, $\sqrt{76}$ is between $8$ and $9$.

This helps us approximate the square root of $76$ to a value between $8$ and $9$. A more precise approximation would place it closer to $8.7$.

Would you like further details on calculating a more exact decimal value for $\sqrt{76}$?

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Further Questions to Explore:

1. How do we calculate a square root to more decimal places?
2. Why is finding the nearest perfect squares helpful in estimation?
3. What other methods can approximate square roots if perfect squares aren’t close?
4. How would this approach change if the number was a perfect square?
5. What role does estimation play in higher-level math calculations?

Tip: For non-perfect squares, narrowing down between two nearby perfect squares provides a good starting point for approximation!