Question

prove root 2 is irrational number ​

Answer 1

Answer:

To prove that the square root of 2 is irrational is to first assume that its negation is true. Therefore, we assume that the opposite is true, that is, the square root of 2 is rational. ... If 2 is a rational number, then we can express it as a ratio of two integers.

Answer 2

Answer:

Step-by-step explanation:

Let us assume that √2 is irrational

then it is of the form √2 = a/b (a , b are co-prime , b ≠0 and a $ b are integers )

b√2 = a

: a = b√2

squaring on  both sides ,

a² = 2b²

2b² = a²

Therefore 2 divides a² and also 2 divides a

So we can write a = 2c for some integer c

substituting  for 'a' we get : 2b² = 4c²

:  b² = 2c²

This means that 2 divides b² , and so 2 divides b

Therefore , a and b have atleast '2' 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√2 IS IRRATIONAL