Theodorus' Lemma

Theodorus' Lemma states that the square root of any odd whole number that is not divisible by 4 (like 3, 5, 7, 9, etc.) cannot be expressed as a simple fraction (meaning it’s irrational). In essence, Theodorus showed that these square roots are irrational numbers, meaning they can’t be exactly written as a ratio of two integers. This was an important step in understanding the nature of irrational numbers within mathematics, confirming that some square roots do not have precise fractional representations.