Estimate the value of 6×2–√. Which of the following choices is the best estimate? Responses:

Question

7.1
6.4
8.4
9.8

Answer 1

To estimate the value of \( 6 \times 2 - \sqrt{6} \), we first calculate each component step-by-step.

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

2. Estimate \( \sqrt{6} \): The square root of 6 is approximately 2.45 (since \( 2^2 = 4 \) and \( 3^2 = 9 \)).

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

Now, we compare this with the given choices:

• 7.1
• 6.4
• 8.4
• 9.8

The closest estimate to \( 9.55 \) is \( 9.8 \). Therefore, the best estimate from the choices is 9.8.