| Irrational Number | Decimal Approximation | Property | Category |
| √2 | 1.4142135623730950488016887242097… | The square root of 2 | Algebraic Irrational |
| √3 | 1.7320508075688772935274463415059… | The square root of 3 | Algebraic Irrational |
| √5 | 2.2360679774997896964091736687313… | The square root of 5 | Algebraic Irrational |
| φ (Golden ratio) | 1.6180339887498948482045868343656… | Divides a line into two parts with a specific ratio | Algebraic Irrational |
| √(2 + √2) | 1.8477590650225735122588520317799… | Nested square root | Algebraic Irrational |
| Continued Fraction of √2 | [1; 2, 2, 2, …] | Continued fraction representation of √2 | Algebraic Irrational |
| π (Pi) | 3.1415926535897932384626433832795… | The ratio of a circle’s circumference to its diameter | Transcendental |
| e (Euler’s number) | 2.7182818284590452353602874713527… | The base of natural logarithms | Transcendental |
| ln(2) | 0.6931471805599453094172321214581… | Natural logarithm of 2 | Transcendental |
| ln(3) | 1.0986122886681096913952452369225… | Natural logarithm of 3 | Transcendental |
| ln(5) | 1.6094379124341003746007593332262… | Natural logarithm of 5 | Transcendental |
| π + e | 5.8598744820488384738233808556322… | Sum of π and e | Transcendental |
| π * e | 8.5397342226735670654635508695463… | Product of π and e | Transcendental |
| π – √2 | 0.7279799588222514799625113035756… | Difference between π and √2 | Transcendental |
| π^2 | 9.8696044010893586188344909998761… | Pi squared | Transcendental |
| √π | 1.7724538509055160272981674833411… | Square root of pi | Transcendental |
| √(π – e) | 1.2733631357053975492476220366719… | Square root of the difference between pi and e | Transcendental |
| e^π | 23.140692632779269005729086367948… | e raised to the power of pi | Transcendental |