Answer:
This proof can be done by contradiction.
Let us assume that 2 - √2 is rational number.
So, by the definition of rational number, we can write it as
where a & b are any integer.
⇒
Since, a and b are integers is also rational.
and therefore √2 is rational number.
This contradicts the fact that √2 is irrational number.
Hence our assumption that 2 - √2 is rational number is false.
Therefore, 2 - √2 is irrational number.
We need to estimate how tall is, on average, one of these object, and then count how many would be in a 5 feet high stack.
For example, on Google you may see that "1.5 cubic foot boxes are the standard box, manufactured by most companies". So, we assume that a standard cardboard box is 1.5 feet tall.
So, if we set the equation
So, there would be between 3 and 4 cardboard boxes in a 5 feet tall stack.
Similarly, we can see that the average book is 9 inches tall. 9 inches are 0.75
feet, so we have
So, there would be between 6 and 7 books in a 5 feet tall stack.
The average brick is 75 millimeters tall, which means 0.25 feet tall. Again, we have
So, there would be 20 bricks in a 5 feet tall stack.
Finally, a coin is about 0.006 feet, which leads to
So, there would be between 833 and 834 coins in a 5 feet tall stack.