Question

Prove that 3-√3 is irrational.

Answer 1

Answer:

Step-by-step explanation:

Let us assume on contrary that " 3 - √3 is a rational number"

∴ 3 - √3 = a/b            where a,b ∈Z , (a,b) = 1 and b≠ 0

  √3 =  3 - a/b

    √3 = (3b - a) /b ⇒ rational number

 ∴√3 is a rational number

But the fact is that " √3 is an irrational number"

Hence our assumption contradicts the fact.

∴ our assumption " 3 - √3 is a rational number"  is wrong.

Hence " 3 - √3 is an irrational number"