Question

Hey guys ... Please maths legends can you solve me this problem - √2 as irrational number !! Thanks @Beautiful68 !!!

Answer 1

hey there is answer
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Answer 2

✴️ HELLO FRIEND ✴️
√√√√√●●●●●√√√√√

To Prove- √2 as 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 is not equal to 0.

Now, √2= a/b
on squaring both side , we get
2= a²/b²
2b² = a²..... equation 1
2 divides a² [ 2 divides 2b²]
2 divides a [ 2 is a prime and divides b² that is 2 divides b]

Let a = 2c for some integer c .
Putting a = 2c in equation 1, we get
2b²= 4c²
b²= 2c²
2 divides b² [ 2 divides 2c²]
2 divides b [ 2 is prime and 2 divides b² so 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.

The contradiction arises by assuming that √2 is rational.

Hence , √2 is irrational.

✌️Hope it helps you ✌️
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