Question

show that root 2 is an irrational number

Answer 1

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Answer 2

Let us assume that √2 is a rational number of the form p/q where q≠0 and are Co primes.

√2=p/q

Squatting =2=p2/q2

Cross multiply
2q2=p2 ----- eq1

(if p divides a2 then p divides a)

As 2 divides p2 then 2 divides p) ------eq2

P=2r
2q2=(2r)2
2q2=4r2
q2=2r2
2 divides q2
2 divides q

From eq1 and eq2 2 is a factor of both q and p

Which is against our assumption that p and q are Co primes. This contradiction arises due to the wrong assumption that √2 is a rational number. Hence √2 is an irrational number.
Hence proved.

Hope it helps you cheers!!