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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?

3 answers

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.

no mine is correct, why is 8.4 correct

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.