Question

The table shows four quantities. Each quantity is assigned a numeric label.

• Order the quantities from least to greatest.

• Next, write the sequence of numeric labels in the same order as their corresponding quantities.

• This sequence of numeric labels is your answer.

• Choose the best answer below. (For example, if the order of the numeric labels were “1, 2, 3, 4,” choose the answer “1234”.)

Answer 1

2341

Explanation:

The fastest way to do this is to simply compute the values for each of the expressions and order them from smallest to largest. We can use approximations

`(\pi^2)/(4) = 2.4674 \approx 2.5 \\` (Label 1)

`(\pi^2)/(8) = (1)/(2) (\pi^2)/(4) \approx (2.5)/(2) \approx 1.25` (Label 2)

`√(2) \approx 1.414` (Label 3)

`√(3) \approx 1.732\\` (Label 4)

So the correct order is

2341