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

Question

6.4
6.4

7.1
7.1

9.8
9.8

8.4

Answer 1

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. Estimate \( \sqrt{6} \). Since \( \sqrt{4} = 2 \) and \( \sqrt{9} = 3 \), we know that \( \sqrt{6} \) is between 2 and 3. For a rough estimate, we can consider it to be about 2.4 (since \( 2.4^2 = 5.76 \) and \( 2.5^2 = 6.25 \)).

3. Now substitute this estimate back: \[ 6 \times 2 - \sqrt{6} \approx 12 - 2.4 = 9.6 \]

Among the given choices, the closest estimate to 9.6 is:

9.8.