Find the Error A classmate estimated  397⎯⎯⎯⎯⎯⎯√
  to be about 200. Explain the mistake and correct it.

 

The classmate estimated 1 of 1.
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 of 397 rather than estimating the square root of 397.

The error your classmate made is that they estimated **397** itself to be around 200, instead of estimating the square root of 397.

Here's a clearer breakdown:

1. The square root of 397 (i.e., \(\sqrt{397}\)) is approximately **19.93**, not anywhere near 200.
2. Your classmate likely confused finding the square root with estimating the value of 397 itself, hence why they arrived at a value near 200. 
3. To correct this mistake, the classmate should have recognized that the square root of a number is much smaller than the number itself. Since \(\sqrt{400} = 20\), it gives a good estimation that \(\sqrt{397}\) is very close to 20.

Would you like more details or explanations on this?

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Here are 5 related questions to expand on this topic:

1. What is the difference between squaring a number and taking its square root?
2. How can we estimate square roots of non-perfect squares like 397?
3. What are the square roots of other numbers near 397, such as 400 or 390?
4. Why do square roots of larger numbers get closer to integers?
5. How does the error in estimating square roots affect real-life applications?

**Tip:** When estimating square roots, find nearby perfect squares (like 400) to get a rough idea of the value.

Find the Error. A classmate estimated the square root of 397 to be about 200. Explain the mistake and correct it.

Discover why estimating the square root of 397 as 200 is incorrect and learn the correct method of estimating square roots. This example covers key mathematical concepts such as square roots, estimation using perfect squares, and the square root theorem. Ideal for Grades 6-8.

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