Question

prove that √2 is an irrational number​

Answer 1

Answer:

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Answer 2

Answer:

to prove $\sqrt{2}$ is irrational

Step-by-step explanation:

let as assume that $\sqrt{2\\}$ is rational number.it is of the form p/q where p&q are integers &q is not equal to 0.where p&q are coprimes

$\sqrt{2} =\frac{p}{q}$

$\sqrt{2q} =p$

squaring on both sides

$(sqrt{2}) ^{2} q^{2} =p^{2}$

$2q^{2} =p^{2} ---------------1$

2 is divisible by$p^{2}$

2 is divisible by p

p=2m----------2

substitude 2 in 1

$q^{2} =2m^{2}$

2 is divisible by $q^{2}$

2 is divisible by q

2 is divisible by both p&q which is contrary to our assumption that $\sqrt{2}$ is rational  and it is a irratonal number