Using rational approximations, what statement is true? (1 point)

Question

O V12 > 1
0 116 > 4
0 116 < 1
0 V12 < 1

Answer 1

To evaluate the statements given, let's first approximate the numbers involved:

1. \( \sqrt{12} \): This value is approximately 3.464 (since \( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \) and \( \sqrt{3} \) is approximately 1.732).

   • Thus, \( \sqrt{12} \) is greater than 3 but less than 4, so \( \sqrt{12} > 1 \).

2. \( 116 \): This is simply the integer 116, which is clearly greater than 4 (since \( 116 > 4 \)).

   • Also, \( 116 > 1 \).

Now, let's analyze each of the statements:

1. \( \sqrt{12} > 1 \): True
2. \( 116 > 4 \): True
3. \( 116 < 1 \): False
4. \( \sqrt{12} < 1 \): False

Based on the above evaluations, the true statements are:

• \( \sqrt{12} > 1 \)
• \( 116 > 4 \)

Since the question seems to require picking one valid statement, both \( \sqrt{12} > 1 \) and \( 116 > 4 \) are true. However, the clear values suggest primarily focusing on the one that is more direct and observable without approximation.

So, the statement that is true is: \( 116 > 4 \).