Question

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Proove that $\sqrt{3$ is an irrational number.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Let us assume that √3 is irrational

then it is of the form √3 = a/b (a , b are co-prime , b ≠0 and a $ b are integers )

b√3 = a

: a = b√3

squaring on  both sides ,

a² = 3b²

3b² = a²

Therefore 3 divides a² and also 3 divides a

So we can write a = 3c for some integer c

substituting  for 'a' we get : 3b² = 9c²

:  b² = 3c²

This means that 3 divides b² , and so 3 divides b

Therefore , a and b have atleast '3' as a common factor .

But this contradicts the fact that a and b are co-prime

So our assumption is incorrect .

SO WE CONCLUDE THAT√3 IS IRRATIONAL