Question

$\sqrt{2} rational \: or \: irrational$
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Answer 1

√2 is an irrational number.

it's decimal expansion is √2= 1.41421........

Hence it doesn't terminate and also is not of the form p/q

Which therefore doesn't satisfy the condition of a number to be rational.

Mark this answer as Brainliest please buddy.

:)

Answer 2

AnswEr :-

• √2 is irrational.

Proof :-

If possible, let √2 be rational and let its simplest form be a/b .

Then, a and b are integers having no common factor other than 1, and b ≠0.

Now, √2 = a/b

=> 2 = a²/b² [ on squaring both sides ]

=> 2b² = a² __i)

=> 2 divides a² [ since, 2 divides 2b² ]

=> 2 divides a [ since, 2 is prime and divides b² => 2 divides b ]

Let a = 2c for some integer c .

Putting a = 2c in eq (i), we get

2b² = 4c²

=> b² = 2c²

=> 2 divides b² [ 2 divides 2c² ]

=> 2 divides b [ since, 2 is prime and 2 divides b² => 2 divides b ]

Thus, 2 is a common factor of a and b

But this contradicts the fact that a and b have no common factor other than 1.

This contradiction arises by assuming that√2 is rational.

Hence, √2 is irrational.

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