Question

$\sqrt{2} \: is \: a \: irrational \: number \:$

Answer 1

Hey mate here is your answer

⤵⤵⤵⤵⤵⤵⤵⤵⤵⤵

yes
it is irrational number

i hope that it is correct
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Answer 2

Answer:

Step-by-step explanation:

To prove ::- √2 is irrational

Solution ::-

Let us assume that √2 is rational. so, it can be expressed as a/b , where a and b are coprimes.

√2 = a /b

2 = a²/b² ..........taking sq. on both sided

a² = 2b²............1

b² = a²/2

Therefore, 2 is a factor of a because it completely divides a

Now, let

a = 2c............here c is some other integer

Putting 2c in equation 1

a² = 2b²

(2c)² = 2b²

4c² = 2b²

4c²/2 = b²

2c² = b²

c² = b²/2

Therefore , 2 is a factor of b because it completely divides b

So, the factor of a and b is 2

But, a and b are coprimes i.e. they cannot have same factors

Hence, our assumption was wrong.

Thus, √2 is irrational.

Hence proved

HOPE IT HELPS YOU!!