Question

show that 3-√2 is irrational​

Answer 1

Answer:

let us assume to the contrary that 3- ✓2 is a rational number then

3 - ✓2 = a/b.

where a and b are co-integers

✓2. = 3 - a/b

✓2 = 3b -a/b

as a and b are integers so it is a rational number so 3b-a/b is also a rational number so ✓2 is also rational number

but as we know ✓2 is irrational so our assumption was wrong and 3-✓2 is irrational