Question

prove that 3-2√3 is irrational number

Answer 1

Answer:

........

Step-by-step explanation:

Let us assume that 3-2√3 is rational.

∴ It can be expressed as:

3-2√3=a/b   (a and b are co-prime- i.e, they have no common factors except 1)

3b-2b√3=a

-2b√3=a-3b

√3=(a-3b)/-2b

But we know that √3 is irrational.

This contradiction has arisen due to our wrong assumption of 3-2√3 being rational.

Hence, we are forced to conclude that 3-2√3 is irrational.