Question

If x is a positive integer, for how many different values of x is sqrt48/x a whole number?

Answer 1

Answer:

The only possible values of x that fulfill with both conditions are 3, 12 and 48.

Step-by-step explanation:

1. What are the positive integers? Also know as the whole numbers or the counting numbers. They start from 1, and continue to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, etc.

2. What are the whole numbers? The definition of whole numbers is that they are the number with no fractions or decimals.

3. According to those definitions, x must be a positive integer and the result of √48/x, must be a whole number.

4. For fulfilling the first condition, x must be only a value from 1 to 48.

5. For fulfilling the second condition, the result of √48/x must be a whole number. It means it must be 1, 2, 3, 4, 5 or 6. From 7 is not possible to continue because those numbers are bigger than 48, for example √49, √64, √81, √100 and so on, and it would be impossible to fulfill with the first condition.

6. So, we have just 6 possible options (√48/x = 1, √48/x = 2, √48/x = 3, √48/x = 4, √48/x = 5 and √48/x =6). Let's review in detail one by one.

√48/x = 1, Is there any value of x for fulfilling both conditions? Yes, it's. It's 48.

√48/x = 1 and let's replace x by 48.

√48/48 = √1 = 1

√48/x = 2, Is there any value of x for fulfilling both conditions? Yes, it's. It's 12.

√48/x = 2 and let's replace x by 12.

√48/12 = √4 = 2

√48/x = 3, Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √9 = 3

√48/x = 4, Is there any value of x for fulfilling both conditions? Yes, it's. It's 3.

√48/x = 4 and let's replace x by 3.

√48/3 = √16 = 4

√48/x = 5 Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √25 = 5

√48/x =6  Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √36 = 6.

The only possible values of x that fulfill with both conditions are 3, 12 and 48.