Irrational Number

Irrational Number

Real number that cannot be written in the form of the ratio $$\frac {a}{b}$$ where $$a$$ and $$b$$ are integers and $$b$$ ≠ 0.

Symbols

The symbol $$\mathbb{Q’}$$ represents the set of irrational numbers and is read as “Q prime”.
The symbol $$\mathbb{Q}$$ represents the set of rational numbers.

Combining rational and irrational numbers gives the set of real numbers: $$\mathbb{Q}$$ U $$\mathbb{Q’}$$ = $$\mathbb{R}$$.

Examples

The numbers $$\sqrt{5}$$, $$\sqrt{11}$$, $$\dfrac{\sqrt{5}}{7}$$, π and e are irrational numbers.

• $$\sqrt{5}$$ = 2.236 067 …
• $$\sqrt{11}$$ = 3.316 624 …
• $$\dfrac{\sqrt{5}}{7}$$ = 0.319 438 …
• π = 3.141 592 …
• e = 2. 718 281 …