Question

Estimate the value of 6×2–√ . Which of the following choices is the best estimate? Responses 7.1 7.1 - 9.8 9.8 - 8.4 8.4 - 6.4

why is 8.4 the correct choice?

Answer 1

no mine is correct, why is 8.4 correct

Answer 2

To estimate the value of \( 6 \times 2 - \sqrt{6} \), let's break it down step by step:

1. Calculate \( 6 \times 2 \):
\[
6 \times 2 = 12
\]

2. Now, estimate \( \sqrt{6} \). Since \( \sqrt{4} = 2 \) and \( \sqrt{9} = 3 \), we know \( \sqrt{6} \) is between 2 and 3. A closer estimate of \( \sqrt{6} \) is approximately \( 2.45 \).

3. Now, subtract \( \sqrt{6} \) from \( 12 \):
\[
12 - \sqrt{6} \approx 12 - 2.45 = 9.55
\]

Now we compare this result (about 9.55) with the given choices:

- 7.1
- 9.8
- 8.4
- 6.4

Out of these options, 9.8 is the closest to our estimate of 9.55.

So there seems to be a misunderstanding in your question regarding 8.4 being the correct choice. Based on the calculation we did, the best estimate is actually 9.8, not 8.4.

Answer 3

I apologize for any confusion in my previous response. Let’s re-examine the expression \(6 \times 2 - \sqrt{6}\).

1. Calculate \(6 \times 2\):
\[
6 \times 2 = 12
\]

2. Estimate \(\sqrt{6}\):
We know that \(\sqrt{6}\) is approximately \(2.45\).

3. Now calculate:
\[
12 - \sqrt{6} \approx 12 - 2.45 \approx 9.55
\]

So, when we find \(12 - \sqrt{6}\), we get approximately 9.55.

However, you are asking why \(8.4\) might be considered a correct option.

Let’s check again to see if there's a possible mistake or rationale that could lead to \(8.4\) being perceived as valid in some context:

If we slightly adjust our estimate for \(\sqrt{6}\) or use more approximative or rounded numbers for further estimations, we may look at:
- For simpler computations:
- \(6 \times 2 = 12\)
- If we take a rougher estimate of \(\sqrt{6}\) closer to \(3\) instead of calculating accurately, we get \(12 - 3 = 9\). This doesn't align with 8.4 as best reasoning, though.

Upon standard calculation and estimation, \(9.55\) gives us the closest approximate to \(9.8\), not \(8.4\).

If you meant a different approach or specific context in which \(8.4\) is relevant, could you clarify how you arrived at that conclusion? Without additional context or a different way to approach the expression, \(9.8\) would ordinarily be the closest estimate.