To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that  students were athletes; therefore,  needs to go in the "athlete" column as the row total. Next, we were told that of those students,  drinks soda; therefore, we need to put  in the "athlete" column and in the "drinks soda" row. Then, we were told that  students were not athletes, but drink soda, so we need to put  in the "not an athlete" column and the "drinks soda" row. Finally, we were told that  students are not athletes or soda drinkers, so  needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following: 

Our question asked how many students were not athletes. We add up the numbers in the "not an athlete" column to get the total:

This means that  students were not athletes. 

A square root asks "what number, when squared, gives you this number?"  So  is asking for which number, when multiplied by itself, is equal to 144.  That number is , since . Note that when the "radical sign" - the bracket surrounding 144 here - is used, mathematically that means that the question is asking for the "principal square root," which means the positive (or "nonnegative") square root.  Technically  also equals , too, but the radical sign tells you that they just want the positive answer, 12.

Here you should see that, were there no decimals, you’d be looking at . But of course there are decimals so it’s not quite that straightforward. When you multiply decimals, you need to count up the decimal places in the input values and that becomes the number of decimal places in the product. Since  has two decimal places, that means that the number to be multiplied by itself should have one.  , so the answer is .

A square root asks you "what number, when squared, gives you this number?"  Here they're asking which number, squared, would give you .  Since , that means that the correct answer is . 

A square root asks "which number, when multiplied by itself, produces this number?" When you're calculating the square root of a decimal, then, it is important to remember what happens when decimals are multiplied  When you multiply decimals, you need to count up the decimal places in the input values and that becomes the number of decimal places in the product. Since  has two decimal places, that means that the number to be multiplied by itself should have one.  , so the answer is .

A square root asks you "what number, when squared, gives you this number?"  Here they're asking which number, squared, would give you .  Since , that means that the correct answer is .

Here the problem is asking you which number, when multiplied by itself, produces . In other words, it's asking you for the square root of , or "what is ?"  

When  is multiplied by , the result is . Meaning that , so .

Note here that the problem asks which of the following COULD be . Technically  is also equal to  so  could also be , and that is why the problem makes that point clear.

A square root asks you "which number, when multiplied by itself, produces this number?" So this problem wants to know which number, when squared, gives you . Note that even if you don't immediately see that , you can use the answer choices to your advantage. You should memorize that  and .  And when numbers that end in zero are squared, they always produce numbers that end in zero, too.  So  and , leaving  as the correct answer.

When you're taking the square root of a fraction, one thing you can do is express it as two different square roots: the square root of the numerator over the square root of the denominator.  So this problem could also be expressed as:

What is ?

Here you can take two fairly straightforward square roots.   and , so your answer is .

A square root asks you "what number, when multiplied by itself, equals this number?"  Here you're told that , meaning that when a number is multiplied by itself, the product doesn't change.  This should get you thinking about two multiplication rules:

Anything times 1 doesn't change. That means that if you want a number to not change when you multiply it, multiply it by 1.  , so  fits the description here.

Anything times 0 equals 0. That means that if you start with 0, whatever you multiply it by you still have 0.  , so  also fits the description here.

Of these, only 1 is an actual answer choice, so 1 is the correct answer.