Between which two consecutive whole numbers does square root of, 53, end square root 
53
​
  lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 53, end square root 
53
​
  to an approximately correct location on the number line.
Real
√53
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_
Answer
Attempt 1 out of 2

Since square root of, end square root 
2
2
​
 
​
  
 equals= 
 and square root of, end square root 
2
2
​
 
​
  
 equals= 
 it is known that square root of, 53, end square root 
53
​
  is between 
 and 


To determine between which two consecutive whole numbers \(\sqrt{53}\) lies, we can first find the square roots of numbers close to 53 that are perfect squares.

### Step 1: Identifying the perfect squares closest to 53
- \(\sqrt{49} = 7\) (since \(7^2 = 49\))
- \(\sqrt{64} = 8\) (since \(8^2 = 64\))

Thus, we know that:
\[
7^2 = 49 \quad \text{and} \quad 8^2 = 64
\]
So, \(\sqrt{53}\) lies between 7 and 8.

### Step 2: Approximation
Since 53 is closer to 49 than 64, \(\sqrt{53}\) is closer to 7 than 8 but still between these two whole numbers.

### Final Answer:
The square root of 53 lies between **7** and **8**. Therefore, the correct sentence would be:

"Since \(\sqrt{49} = 7\) and \(\sqrt{64} = 8\), it is known that \(\sqrt{53}\) is between 7 and 8."

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Would you like to go into more detail about approximating square roots? 

Here are 5 questions to further explore this topic:
1. What is the approximate value of \(\sqrt{53}\) to one decimal place?
2. How would you estimate the square root of non-perfect square numbers?
3. What methods can be used to find more precise square root values?
4. How can the concept of perfect squares help in estimating square roots?
5. What are some real-world applications of estimating square roots?

**Tip**: When estimating square roots of non-perfect squares, always find the perfect squares on either side of the number!

Between which two consecutive whole numbers does the square root of 53 lie? Fill out the sentence below to justify your answer and use your mouse to drag the square root of 53 to an approximately correct location on the number line.

Find out between which two whole numbers the square root of 53 lies. This problem helps in estimating square roots using perfect squares, a key concept in middle school math. Suitable for Grades 6-8.

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