To determine between which two consecutive whole numbers the square root of 65 lies, we need to find the closest perfect squares around 65.

Step 1: Find the nearest perfect squares.

• $8^2 = 64$
• $9^2 = 81$

Since $64 < 65 < 81$, we know that:

$8 < \sqrt{65} < 9$

Step 2: Approximate the square root of 65.

Since 65 is very close to 64, the value of $\sqrt{65}$ will be slightly more than 8.
Using a calculator:

$\sqrt{65} \approx 8.06$

Final Answer:

The square root of 65 lies between the consecutive whole numbers 8 and 9.

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Here are 5 related questions to explore:

1. What is the square root of 70, and between which numbers does it lie?
2. How do you estimate square roots without a calculator?
3. Why are square roots of non-perfect squares irrational numbers?
4. What is the square root of 64 and how does it compare to 65?
5. Can you express $\sqrt{65}$ as a fraction?

Tip: The closer a number is to a perfect square, the easier it is to estimate its square root!