Finding an Irrational Number Between Two Irrational Numbers

Irrational numbers are non-terminating and non-repeating decimal numbers. They cannot be expressed in the form of p/q, where p and q are integers. Here's how to find an irrational number between any two irrational numbers:

Step 1: Find the difference between the two irrational numbers.

Let's say the two irrational numbers are a and b. Find the difference between them by subtracting b from a: d = a - b.

Step 2: Divide the difference by 2.

Divide the difference by 2 to get d/2.

Step 3: Add the result to the smaller of the two numbers.

Add the result of d/2 to the smaller of the two numbers. Let's call this number c. So, c = smaller number + d/2.

Step 4: Check if the result is irrational.

Check if the result is irrational by checking if it is a non-terminating and non-repeating decimal number. If it is, then you have found an irrational number between a and b.

Step 5: Repeat the process if needed.

If the result is not irrational, then repeat the process by choosing a new smaller number and finding the difference between the two irrational numbers. Then, divide the difference by 2 and add it to the smaller number to find a new result.

Conclusion

In conclusion, finding an irrational number between any two irrational numbers involves finding the difference between the two numbers, dividing the difference by 2, adding the result to the smaller number, and checking if the result is irrational. Repeat the process if needed until an irrational number is found.

There is a formula:-
1/2(x+y)
In this x