What are three irrational numbers between 2 and 3?

Three irrational numbers between 2 and 3 are √5, e, and π − 1. An irrational number cannot be written as a simple fraction and its decimal never ends or repeats. Many such numbers lie between 2 and 3. Good examples are √5 ≈ 2.236…, e ≈ 2.718… (Euler’s number), and π − 1 ≈ 2.14159…. All of these are well known to be irrational and clearly fall in the open interval (2, 3).

Why these are irrational

• √5: square root of a non-perfect square is irrational.
• e: base of natural logarithms; proven irrational and even transcendental.
• π − 1: π is irrational; subtracting 1 keeps it irrational.

More examples you can build

• √6 ≈ 2.449…, √7 ≈ 2.6457…
• 2 + √2 − 1 ≈ 2.414… (since √2 is irrational)
• 2 + 1/√2 ≈ 2.707… (still irrational)