Question

prove 2-✓2 is irrational by using contradiction method ​

Answer 1

Answer:

Step-by-step explanation:

Let 2-√2 a rational number

So 2-√2 = p/q (where q aand p are non primes are q is equal to non zero)

√2 = -(p/q)-2

We know that √2 IA rational number but -(p/q)-2 is rational

So it is contradiction

So 2-√2 is a rational number.

Answer 2

let 2-√2 be rational

now 2-√2=a/b. ,where a and b are integer and co prime no.

-√2=a/b-2

-√2=a-2b/b

(we know a-2b/b is rational no.

so is the -√2 is rational )

but this contradicts the fact that √2is irrational .

this contradiction has arisen due to our wrong assumption that 2-√2 is rational.

Therefore I conclude that

2-√2 is irrational.