Question

prove it.. √2 is an irrational number with graph...​

Answer 1

Let √2 be a rational number.

A rational number can be written in the form of p/q.

√2 = p/q

p = √2q

Squaring on both sides,

p²=2q²

2 divides p² then 2 also divides p.

So, p is a multiple of 2.

p = 2a (a is any integer)

Put p=2a in p²=2q²

(2a)² = 2q²

4a² = 2q²

2a² = q²

2 divides q² then 2 also divides q.

Therefore,q is also a multiple of 2.

So, q = 2b

Both p and q have 2 as a common factor.

But this contradicts the fact that p and q are co primes.

So our supposition is false.

Therefore, √2 is an irrational number.

Hence proved.

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