Question

how to prove root 2​

Answer 1

ANSWER:

Here you can read a step-by-step proof with simple explanations for the fact that the square root of 2 is an irrational number. It is the most common proof for this fact and is by contradiction.

How do we know that square root of 2 is an irrational number? In other words, how do we know that √2 doesn't have a pattern in its decimal sequence? Maybe the pattern is very well hidden and is really long, billions of digits.

Answer 2

Step-by-step explanation:

A proof that the square root of 2 is irrational. Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.