Between which two consecutive whole numbers does square root of, 65, end square root65​ lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 65, end square root65​ to an approximately correct location on the number line.

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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Do you want me to plot it on a sample number line or assist further? 

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!

Between which two consecutive whole numbers does the square root of 65 lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of 65 to an approximately correct location on the number line.

Learn how to determine between which two consecutive whole numbers the square root of 65 lies. This detailed explanation includes perfect squares, square root approximation, and number line visualization, suitable for students in Grades 6-8.

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