Question

select the correct answer.

which of these numbers is the most precise approximation of \\(\sqrt{12}\\)?

3.0
3.446
3.46
3.464

Explanation:

Calculate the square root of 12

$$ \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} $$

$$ \sqrt{3} \approx 1.7320508 $$

$$ \sqrt{12} \approx 2 \times 1.7320508 = 3.4641016 $$

Compare with given options

• Option 1: \(3.0\) (error \(\approx 0.464\))
• Option 2: \(3.446\) (error \(\approx 0.018\))
• Option 3: \(3.46\) (error \(\approx 0.004\))
• Option 4: \(3.464\) (error \(\approx 0.0001\))

Identify the most precise approximation

$$ |3.4641016 - 3.464| = 0.0001016 \text{ (smallest error)} $$

Answer:

• 3.0
• 3.446
• 3.46
• 3.464 (Correct answer)