Between the numbers 1 and 6, there are infinitely many irrational numbers. An irrational number is any real number that cannot be expressed as a simple fraction of two integers. This means that the digits in its decimal representation go on forever without repeating.
For example, the square root of 2 (√2) is an irrational number, and it lies between 1 and 6 since √2 is approximately 1.414. Similarly, the square root of 3 (√3) is also an irrational number and is approximately 1.732, again falling within this range.
Moreover, we can find countless other examples like π (pi), which is approximately 3.14, and e (Euler’s number), which is approximately 2.718. These irrational numbers can be found in a continuous fashion. Given that between any two rational numbers there are infinitely many irrational numbers, it follows that between 1 and 6, there are also infinitely many irrational numbers.