Question

Prove hat root 2 is irrational

Answer 1

$\huge\bf\blue{Answer}$

Proof that the square root of 2 is irrational. Assume is rational, i.e. it can be expressed as a rational fraction of the form , where and are two relatively prime integers. ... However, two even numbers cannot be relatively prime, so cannot be expressed as a rational fraction; hence is irrational.

$\huge\bf\blue{Or,}$

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.

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