To approximate the square root of 95, we can follow these steps:

Step 1: Find two perfect squares around 95

• The perfect square just below 95 is $81$, because $\sqrt{81} = 9$.
• The perfect square just above 95 is $100$, because $\sqrt{100} = 10$.

Therefore, the square root of 95 must lie between the whole numbers 9 and 10.

You can input these values into the sentence as:

• "The square root of 95 must lie between the whole numbers 9 and 10."

Would you like to go further into how we can refine the estimate? Let me know if you'd like more details!

---

Additional Related Questions:

1. How can we use the method of averaging to refine the estimate for $\sqrt{95}$?
2. What is the next step in the approximation process after finding the whole numbers 9 and 10?
3. How would the process change if we were approximating the square root of a larger number like 150?
4. How can we estimate square roots for numbers that aren't perfect squares?
5. How does the difference between consecutive perfect squares affect the accuracy of our estimate?

Tip:

If you're estimating square roots, using the method of averaging between your lower and upper bounds is an effective way to narrow down to the correct value!