Question

Show that 3-√2 is an irrational​

Answer 1

Answer:

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

Now, 3 - √2 = a/b

[Here a and b are co-prime numbers]

√2 = [3 - (a/b)]

√2 = [(3b - a)/b]

Here, [(3b - a)] is a rational number.

But we know tthat√2 is an irrational number.

So, [(3b - a)] is also a irrational number.

So, our assumption is wrong and 3 - √2 is an irrational number.

Hence, proved.