Can you explain simply how to find an irrational number between two rational whole numbers?

Answer 1

To find an irrational number between two rational whole numbers, you can follow these steps:

1. Choose any two rational whole numbers. For example, let's say you choose 2 and 3.

2. Calculate the average (or mean) of the two chosen numbers. In this case, add the numbers and divide by 2: (2 + 3) / 2 = 2.5.

3. The resulting value of 2.5 is a rational number. However, to find an irrational number, we need to make it irrational.

4. One method to make it irrational is by taking the square root of a prime number that is not a perfect square. For example, √2 is an irrational number.

5. Multiply the square root of a prime number by the average you calculated: 2.5 * √2.

6. The product, 2.5 * √2, is an irrational number between the two chosen rational whole numbers.

So, by following these steps, you can find an irrational number between any two given rational whole numbers.