Question

show that 3- √2 is irrational​

Answer 1

Answer:

We know that √2is an irrational number.

Let us assume to the contrary that 3-√2 is a rational number.

so, 3-√2=a/b

√2=3-a/b

√2=(3b-a)/b

We know that (3b-a)/b is a rational number so √2is a rational number. This contradicts the fact that √2 is a rational number. This contradiction has arisen because of our wrong assumption that 3-√2 is a rational number so 3-√2 is an irrational number.